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# The Matrix

The Matrix is a 1999 science fiction action film written and directed by The Wachowskis[note 1] and starring Keanu Reeves, Laurence Fishburne, Carrie-Anne Moss, Hugo Weaving, and Joe Pantoliano. It depicts a dystopian future in which humanity is unknowingly trapped inside a simulated reality called the Matrix, created by thought-capable machines (artificial beings)[note 2] to control humans while using their bodies as an energy source.[4] Hacker and computer programmer Neo learns this truth and "is drawn into a rebellion against the machines",[5] which involves other people who have been freed from the Matrix.

The film is an example of the cyberpunk subgenre.[6] The Wachowskis' approach to action scenes drew upon their admiration for Japanese animation[7] and martial arts films, and the film's use of fight choreographers and wire fu techniques from Hong Kong action cinema influenced subsequent Hollywood action film productions. The Matrix is known for popularizing a visual effect known as "bullet time", in which the heightened perception of certain characters is represented by allowing the action within a shot to progress in slow-motion while the camera's viewpoint appears to move through the scene at normal speed. The film contains numerous allusions to philosophical and religious ideas, including existentialism, Marxism, feminism, Buddhism, nihilism, and postmodernism.[8][9] While some critics have praised the film for its handling of difficult subjects, others characterize the film's themes as being largely overshadowed by its action scenes.[10]

The Matrix was first released in the United States on March 31, 1999 and grossed over $460 million worldwide. It was well-received by many critics[11][12] and won four Academy Awards, as well as other accolades, including BAFTA Awards and Saturn Awards. The Matrix was praised for its innovative visual effects, cinematography and entertainment value. The film has since appeared in lists of the greatest science fiction films,[13][14][15] and, in 2012, was added to the National Film Registry for preservation.[16] The success of the film led to the release of two feature film sequels, both written and directed by the Wachowskis: The Matrix Reloaded and The Matrix Revolutions. The Matrix franchise was further expanded through the production of comic books, video games and animated short films, in which the Wachowskis were heavily involved, and even inspired books and theories on ideas in religion and philosophy. The Matrix Theatrical release poster Directed byThe Wachowski Brothers Produced byJoel Silver Written byThe Wachowski Brothers Starring Music byDon Davis CinematographyBill Pope Edited byZach Staenberg Production companies Distributed by Release date • March 31, 1999 (United States) • April 8, 1999 (Australia) Running time 136 minutes[1] Country LanguageEnglish Budget$63 million[3]

### Pre-production

The actors of the film were required to be able to understand and explain The Matrix.[32] French philosopher Jean Baudrillard's Simulacra and Simulation was required reading for most of the principal cast and crew.[35] Reeves stated that the Wachowskis had him read Simulacra and Simulation, Kevin Kelly's Out of Control: The New Biology of Machines, Social Systems, and the Economic World, and Dylan Evans’s ideas on evolutionary psychology even before they opened up the script,[17] and eventually he was able to explain all the philosophical nuances involved.[32] Moss commented that she had difficulty with this process.[17]

The directors had also been admirers of Hong Kong action cinema for a long time, so they decided to hire the Chinese martial arts choreographer and film director Yuen Woo-ping to work on fight scenes. To prepare for the wire fu, the actors had to train hard for several months.[32] The Wachowskis first scheduled four months for training. Yuen was optimistic but then began to worry when he realized how unfit the actors were.[25]

Yuen let their body style develop and then worked with each actor's strength. He built on Reeves' diligence, Fishburne's resilience, Weaving's precision, and Moss's feminine grace.[25] Yuen designed Moss' moves to suit her deftness and lightness.[36] Prior to the pre-production, Reeves suffered a two-level fusion of his cervical spine which had begun to cause paralysis in his legs, requiring him to undergo neck surgery. He was still recovering by the time of pre-production, but he insisted on training, so Yuen let him practice punches and lighter moves. Reeves trained hard and even requested training on days off. However, the surgery still made him unable to kick for two out of four months of training. As a result, Reeves did not kick much in the film.[25] Weaving had to undergo hip surgery after he sustained an injury during the training process.[32]

### Production design

In the film, the code that composes the Matrix itself is frequently represented as downward-flowing green characters. This code uses a custom typeface designed by Simon Whiteley,[34] which includes mirror images of half-width kana characters and Western Latin letters and numerals.[9] In a 2017 interview at CNET, he attributed the design to his wife, who's from Japan, and added, "I like to tell everybody that The Matrix's code is made out of Japanese sushi recipes".[37] "The color green reflects the green tint commonly used on early monochrome computer monitors".[38] Lynne Cartwright, the Visual Effects Supervisor at Animal Logic, supervised the creation of the film's opening title sequence, as well as the general look of the Matrix code throughout the film, in collaboration with Lindsay Fleay and Justen Marshall.[34] The portrayal resembles the opening credits of the 1995 Japanese cyberpunk film, Ghost in the Shell, which had a strong influence on the Matrix series (see below).[9] It was also used in the subsequent films, on the related website, and in the game The Matrix: Path of Neo, and its drop-down effect is reflected in the design of some posters for the Matrix series. The code received the Runner-up Award in the 1999 Jesse Garson Award for In-film typography or opening credit sequence.[34]

The Matrix's production designer, Owen Paterson, used methods to distinguish the "real world" and the Matrix in a pervasive way. The production design team generally placed a bias towards the Matrix code's distinctive green color in scenes set within the simulation, whereas there is an emphasis on the color blue during scenes set in the "real world". In addition, the Matrix scenes' sets were slightly more decayed, monolithic, and grid-like, to convey the cold, logical and artificial nature of that environment. For the "real world", the actors' hair was less styled, their clothing had more textile content, and the cinematographers used longer lenses to soften the backgrounds and emphasize the actors.[9]

The Nebuchadnezzar was designed to have a patched-up look, instead of clean, cold and sterile space ship interior sets as used on films like Star Trek. The wires were made visible to show the ship's working internals, and each composition was carefully designed to convey the ship as "a marriage between Man and Machine".[39] For the scene when Neo wakes up in the pod connected to the Matrix, the pod was constructed to look dirty, used, and sinister. During the testing of a breathing mechanism in the pod, the tester suffered hypothermia in under eight minutes, so the pod had to be heated.[40]

Kym Barrett, costume designer, said that she defined the characters and their environment by their costume.[41] For example, Reeves' office costume was designed for Thomas Anderson to look uncomfortable, disheveled, and out of place.[42] Barrett sometimes used three types of fabric for each costume, and also had to consider the practicality of the acting. The actors needed to perform martial art actions in their costume, hang upside-down without people seeing up their clothing, and be able to work the wires while strapped into the harnesses.[41] For Trinity, Barrett experimented with how each fabric absorbed and reflected different types of light, and was eventually able to make Trinity's costume mercury-like and oil-slick to suit the character.[36] For the Agents, their costume was designed to create a secret service, undercover look, resembling the film JFK.[43]

The sunglasses, a staple to the film's aesthetics, were commissioned for the film by designer Richard Walker from sunglass maker Blinde Design.[44]

### Filming

All but a few scenes were filmed at Fox Studios in Sydney, and in the city itself, although recognizable landmarks were not included in order to maintain the impression of a generic American city. The filming helped establish New South Wales as a major film production center.[45] Filming commenced in March 1998 and wrapped in August 1998; principal photography took 118 days.[40]

Due to Reeves' neck injury, some of the action scenes had to be rescheduled to wait for his full recovery. As a result, the filming began with scenes that did not require much physical exertion,[42] such as the scene in Thomas Anderson's office, the interrogation room,[43] or the car ride in which Neo is taken to see the Oracle.[46] Locations for these scenes included Martin Place's fountain in Sydney, half-way between it and the adjacent Colonial Building, and the Colonial Building itself.[47] During the scene set on a government building rooftop, the team filmed extra footage of Neo dodging bullets in case the bullet time process did not work. The bullet-time fight scene was filmed on the roof of Symantec Corporation building in Kent Street, opposite of Sussex street.[48]

Moss performed the shots featuring Trinity at the beginning of the film and all the wire stunts herself.[36] The rooftop set that Trinity uses to escape from Agent Brown early in the film was left over from the production of Dark City, which has prompted comments due to the thematic similarities of the films.[49] During the rehearsal of the lobby scene, in which Trinity runs on a wall, Moss injured her leg and was ultimately unable to film the shot in one take. She stated that she was under a lot of pressure at the time and was devastated when she realized that she would be unable to do it.[50]

The dojo set was built well before the actual filming. During the filming of these action sequences, there was significant physical contact between the actors, earning them bruises. Because of Reeves's injury and his insufficient training with wires prior to the filming, he was unable to perform the triple kicks satisfactorily and became frustrated with himself, causing the scene to be postponed. The scene was shot successfully a few days later, with Reeves using only three takes. Yuen altered the choreography and made the actors pull their punches in the last sequence of the scene, creating a training feel.[51]

The filmmakers originally planned to shoot the subway scene in an actual subway station, but the complexity of the fight and related wire work required shooting the scene on a set. The set was built around an existing train storage facility, which had real train tracks. Filming the scene when Neo slammed Smith into the ceiling, Chad Stahelski, Reeves' stunt double, sustained several injuries, including broken ribs, knees, and a dislocated shoulder. Another stuntman was injured by a hydraulic puller during a shot where Neo was slammed into a booth.[52] The office building in which Smith interrogated Morpheus was a large set, and the outside view from inside the building was a large, three story high cyclorama. The helicopter was a full-scale light-weight mock-up suspended by a wire rope operated a tilting mechanism mounted to the studio roofbeams. The helicopter had side mounted to it a real minigun, which was set to cycle at half normal full (3000 rounds per min) firing rate. The visual effect of the helicopters rotating blades was effected by using strobe lighting.[53]

To prepare for the scene in which Neo wakes up in a pod, Reeves lost 15 pounds and shaved his whole body to give Neo an emaciated look. The scene in which Neo fell into the sewer system concluded the principal photography.[40] According to The Art of the Matrix, at least one filmed scene and a variety of short pieces of action were omitted from the final cut of the film.[54]

### Visual effects

The "bullet time" effect was created for the film. A scene would be computer modeled to decide the positioning of the physical cameras. The actor then provided their performance in a chroma key setup, while the cameras were fired in rapid succession, with fractions of a second delay between each shot. The result was combined with CGI backgrounds to create the final effect at (0:33).

As for artistic inspiration for bullet time, I would credit Otomo Katsuhiro, who co-wrote and directed Akira, which definitely blew me away, along with director Michel Gondry. His music videos experimented with a different type of technique called view-morphing and it was just part of the beginning of uncovering the creative approaches toward using still cameras for special effects. Our technique was significantly different because we built it to move around objects that were themselves in motion, and we were also able to create slow-motion events that 'virtual cameras' could move around – rather than the static action in Gondry's music videos with limited camera moves.

The film is known for popularizing a visual effect[56] known as "bullet time", which allows a shot to progress in slow-motion while the camera appears to move through the scene at normal speed.[57] Bullet time has been described as "a visual analogy for privileged moments of consciousness within the Matrix",[58] and throughout the film, the effect is used to illustrate characters' exertion of control over time and space.[59] The Wachowskis first imagined an action sequence that slowed time while the camera pivoted rapidly around the subjects, and proposed the effect in their screenplay for the film. When John Gaeta read the script, he pleaded with an effects producer at Manex Visual Effects to let him work on the project, and created a prototype that led to him becoming the film's visual effects supervisor.[60]

The method used for creating these effects involved a technically expanded version of an old art photography technique known as time-slice photography, in which an array of cameras are placed around an object and triggered simultaneously. Each camera captures a still picture, contributing one frame to the video sequence, which creates the effect of "virtual camera movement"; the illusion of a viewpoint moving around an object that appears frozen in time.[57]

The bullet time effect is similar but slightly more complicated, incorporating temporal motion so that rather than appearing totally frozen, the scene progresses in slow and variable motion.[55][60] The cameras' positions and exposures were previsualized using a 3D simulation. Instead of firing the cameras simultaneously, the visual effect team fired the cameras fractions of a second after each other, so that each camera could capture the action as it progressed, creating a super slow-motion effect.[57] When the frames were put together, the resulting slow-motion effects reached a frame frequency of 12,000 per second, as opposed to the normal 24 frames per second of film.[32] Standard movie cameras were placed at the ends of the array to pick up the normal speed action before and after. Because the cameras circle the subject almost completely in most of the sequences, computer technology was used to edit out the cameras that appeared in the background on the other side.[57] To create backgrounds, Gaeta hired George Borshukov, who created 3D models based on the geometry of buildings and used the photographs of the buildings themselves as texture.

The photo-realistic surroundings generated by this method were incorporated into the bullet time scene,[60] and linear interpolation filled in any gaps of the still images to produce a fluent dynamic motion;[61] the computer-generated "lead in" and "lead out" slides were filled in between frames in sequence to get an illusion of orbiting the scene.[62] Manex Visual Effects used a cluster farm running the Unix-like operating system FreeBSD to render many of the film's visual effects.[63][64]

Manex also handled creature effects, such as Sentinels and machines in real world scenes; Animal Logic created the code hallway and the exploding Agent at the end of the film. DFilm managed scenes that required heavy use of digital compositing, such as Neo's jump off a skyscraper and the helicopter crash into a building. The ripple effect in the latter scene was created digitally, but the shot also included practical elements, and months of extensive research were needed to find the correct kind of glass and explosives to use. The scene was shot by colliding a quarter-scale helicopter mock-up into a glass wall wired to concentric rings of explosives; the explosives were then triggered in sequence from the center outward, to create a wave of exploding glass.[65]

The photogrametric and image-based computer-generated background approaches in The Matrix's bullet time evolved into innovations unveiled in the sequels The Matrix Reloaded and The Matrix Revolutions. The method of using real photographs of buildings as texture for 3D models eventually led the visual effect team to digitize all data, such as scenes, characters' motions and expressions. It also led to the development of "Universal Capture", a process which samples and stores facial details and expressions at high resolution. With these highly detailed collected data, the team were able to create virtual cinematography in which characters, locations, and events can all be created digitally and viewed through virtual cameras, eliminating the restrictions of real cameras.[60]

### Sound effects and music

Dane A. Davis was responsible for creating the sound effects for the film. The fight scenes sound effects, such as the whipping sounds of punches were created using thin metal rods and recording them, then editing the sounds. The sound of the pod containing a human baby closing required almost fifty sounds put together.[66]

The film's score was composed by Don Davis.[67][68] He noted that mirrors appear frequently in the film: reflections of the blue and red pills are seen in Morpheus's glasses; Neo's capture by Agents is viewed through the rear-view mirror of Trinity's Triumph Speed Triple motorcycle; Neo observes a broken mirror mending itself; reflections warp as a spoon is bent; the reflection of a helicopter is visible as it approaches a skyscraper. Davis focused on this theme of reflections when creating his score, alternating between sections of the orchestra and attempting to incorporate contrapuntal ideas. Davis' score combines orchestral, choral and synthesizer elements; the balance between these elements varies depending on whether humans or machines are the dominant subject of a given scene.[69] In addition to Davis' score, The Matrix soundtrack also features music from acts such as Rammstein, Rob Dougan, Rage Against the Machine, Propellerheads, Ministry, Deftones, Monster Magnet, The Prodigy, Rob Zombie, Meat Beat Manifesto, and Marilyn Manson.[70][71][72]

## Influences

The fact that The Matrix draws from and alludes to numerous cinematic and literary works, and concepts from mythology, religion and philosophy, including the ideas of Buddhism, Christianity, Gnosticism, Hinduism, and Judaism.[73] has led to the suggestion by some writers and critics that it is more than a work of entertainment, because it deals with very important ideas.

Amongst these possible allusions, it is suggested that the name of the character Trinity refers to Christianity's doctrine of the Trinity.[74] Andrew Godoski [75] sees allusions to Christ, including Neo's "virgin birth", his doubt in himself, the prophecy of his coming, along with many other Christian references.[32]

In The Matrix, a copy of Jean Baudrillard's philosophical work Simulacra and Simulation, which was published in French in 1981, is visible on-screen as "the book used to conceal disks",[76][35] and Morpheus quotes the phrase "desert of the real" from it.[77] "The book was required reading for"[78] the actors prior to filming.[35][79] However, Baudrillard himself said that The Matrix misunderstands and distorts his work.[77][80] Some interpretors of The Matrix mention Baudrillard's philosophy to support their claim "that the [film] is an allegory for contemporary experience in a heavily commercialized, media-driven society, especially in developed countries".[81] "The influence of [Baudrillard] was brought to the public's attention through the writings of art historians such as Griselda Pollock and film theorists such as Heinz-Peter Schwerfel".[82] In addition to Baudrillard, the Wachowskis' were also significantly influenced by Kevin Kelly's Out of Control: The New Biology of Machines, Social Systems, and the Economic World, and Dylan Evans’s ideas on evolutionary psychology.[17]

The Matrix belongs to the cyberpunk genre of science fiction,and draws from earlier works in the genre such as the 1984 novel Neuromancer by William Gibson.[6] For example, the film's use of the term "Matrix" is adopted from Gibson's novel,[83] though L. P. Davies had already used the term "Matrix" fifteen years earlier for a similar concept in his 1969 novel The White Room ("It had been tried in the States some years earlier, but their 'matrix' as they called it hadn't been strong enough to hold the fictional character in place").[84] After watching The Matrix, Gibson commented that the way that the film's creators had drawn from existing cyberpunk works was "exactly the kind of creative cultural osmosis" he had relied upon in his own writing;[6] however, he noted that the film's Gnostic themes distinguished it from Neuromancer, and believed that The Matrix was thematically closer to the work of science fiction author Philip K. Dick.[6] Other writers have also commented on the similarities between The Matrix and Dick's work;[85][86][87] one example of such influence is a Philip K. Dick's 1977 conference, in which he stated: "We are living in a computer-programmed reality, and the only clue we have to it is when some variable is changed, and some alteration in our reality occurs".[88][89][90][91]

The Wachowskis' approach to action scenes drew upon their admiration for Japanese animation such as Ninja Scroll and Akira.[7] Director Mamoru Oshii's 1995 animated film Ghost in the Shell was a particularly strong influence;[7] producer Joel Silver has stated that the Wachowskis first described their intentions for The Matrix by showing him that anime and saying, "We wanna do that for real".[92][93] Mitsuhisa Ishikawa of Production I.G, which produced Ghost in the Shell, noted that the anime's high-quality visuals were a strong source of inspiration for the Wachowskis. He also commented, "... cyberpunk films are very difficult to describe to a third person. I'd imagine that The Matrix is the kind of film that was very difficult to draw up a written proposal for to take to film studios". He stated that since Ghost in the Shell had gained recognition in America, the Wachowskis used it as a "promotional tool".[94] The action scenes of The Matrix were also strongly influenced by live-action films such as those of director John Woo.[85] The martial arts sequences were inspired by Fist of Legend, a critically acclaimed 1995 martial arts film starring Jet Li. The fight scenes in Fist of Legend led to the hiring of Yuen as fight choreographer.[95][96]

The film makes several references to Lewis Carroll's Alice's Adventures in Wonderland.[97] The pods in which the machines keep humans have been compared to images in Metropolis, and the work of M. C. Escher.[98] The Wachowskis have described Stanley Kubrick's 2001: A Space Odyssey as a formative cinematic influence, and as a major inspiration on the visual style they aimed for when making The Matrix.[99][100][101] Reviewers have also commented on similarities between The Matrix and other late-1990s films such as Strange Days, Dark City, and The Truman Show.[102][103][104][105][106] Comparisons have also been made to Grant Morrison's comic series The Invisibles; Morrison believes that the Wachowskis essentially plagiarized his work to create the film.[107] Comparisons have also been made between The Matrix and the books of Carlos Castaneda.[108] The similarity of the film's central concept to a device in the long-running series Doctor Who has also been noted. As in the film, the Matrix of that series (introduced in the 1976 serial The Deadly Assassin) is a massive computer system which one enters using a device connecting to the head, allowing users to see representations of the real world and change its laws of physics; but if killed there, they will die in reality.[109]

### Philosophical influences

It has been suggested by philosopher William Irwin that the idea of the "Matrix" – a generated reality invented by malicious machines – is an allusion to Descartes' "First Meditation", and his idea of an evil demon. The Meditation hypothesizes that the perceived world might be a comprehensive illusion created to deceive us.[8] The same premise can be found in Hilary Putnam's brain in a vat scenario proposed in the 1980s.[8] A connection between the premise of The Matrix and Plato's Allegory of the Cave has also been suggested. The allegory is related to Plato's theory of Forms, which holds that the true essence of an object is not what we perceive with our senses, but rather its quality, and that most people perceive only the shadow of the object and are thus limited to false perception.[32]

The philosophy of Immanuel Kant has also been claimed as another influence on the film, and in particular how individuals within the Matrix interact with one another and with the system. Kant states in his Critique of Pure Reason that people come to know and explore our world through synthetic means (language, etc.), and thus this makes it rather difficult to discern truth from falsely perceived views. This means people are their own agents of deceit, and so in order for them to know truth, they must choose to openly pursue truth. this idea can be examined in Agent Smith's monologue about the first version of the Matrix, which was designed as a human utopia, a perfect world without suffering and with total happiness. Agent Smith explains that, "it was a disaster. No one accepted the program. Entire crops [of people] were lost." The machines had to amend their choice of programming in order to make people subservient to them, and so they conceived the Matrix in the image of the world in 1999. The world in 1999 was far from a utopia, but still humans accepted this over the suffering-less utopia. According to William Irwin this is Kantian, because the machines wished to impose a perfect world on humans in an attempt to keep people content, so that they would remain completely submissive to the machines, both consciously and subconsciously, but humans were not easy to make content.[110]

It has also been noted that the character Morpheus paraphrases the Chinese taoist philosopher Zhuangzi when he asks Neo, “Have you ever had a dream, Neo, that you were so sure was real? What if you weren’t able to wake from that dream? How would you know the difference from the real world and the dream world?”[111]

## Release

The Matrix was released on VHS and DVD on December 7, 1999.[3] It was also released on Laserdisc in its original aspect ratio of 2.35:1 on September 21, 1999 in the US from Warner Home Video as well as in a cropped 1.33:1 aspect ratio in Hong Kong from ERA Home Entertainment. After its DVD release, it was the first DVD to sell more than one million copies in the US,[112] and went on to be the first to sell more than three million copies in the US.[32] By November 10, 2003, one month after The Matrix Reloaded DVD was released, the sales of The Matrix DVD had exceeded 30 million copies.[113] The Ultimate Matrix Collection was released on HD DVD on May 22, 2007[112] and on Blu-ray on October 14, 2008.[114] The film was also released standalone in a 10th anniversary edition Blu-ray in the Digibook format on March 31, 2009, 10 years to the day after the film was released theatrically.[115] In 2010, the film had another DVD release along with the two sequels as The Complete Matrix Trilogy.

## Reception

### Box office

The film earned $171,479,930 (37.0%) in the United States and Canada and$292,037,453 (63.0%) in other countries, for a worldwide total of $463,517,383.[3] In North America, it became the fifth highest grossing film of 1999 and the highest grossing R-rated film of 1999. Worldwide it was the fourth highest grossing film of the year.[3] As of 2012 it was placed 122nd on the list of highest grossing films of all time, and the second highest grossing film in the Matrix franchise after The Matrix Reloaded ($742.1 million).[3]

### Critical response

The Matrix was praised by many critics, as well as filmmakers, and authors of science fiction,[12] especially for its "spectacular action" scenes and its "groundbreaking special effects". Some have described The Matrix as one of the greatest science fiction films of all time,[13][14] Entertainment Weekly called The Matrix "the most influential action movie of the generation".[26] There have also been those, including philosopher William Irwin, who have suggested that the film explores significant philosophical and spiritual themes. However, other reviewers described The Matrix as "simple-minded fun" and "another slice of overlong, high concept hokum". Review aggregator Rotten Tomatoes reported an 88% of positive reviews, with a weighted average score of 7.6/10 based upon a sample of 144 reviews. The site's critical consensus reads, "Thanks to the Wachowskis' imaginative vision, The Matrix is a smartly crafted combination of spectacular action and groundbreaking special effects".[11] At Metacritic, which assigns a rating out of 100 to reviews from mainstream critics, the film received a score of 73 based on 35 reviews, indicating "generally favorable reviews."[12] Audiences polled by CinemaScore gave the film an average grade of "A-" on an A+ to F scale.[116] It ranked 323rd among critics, and 546th among directors, in the 2012 Sight & Sound polls of the greatest films ever made.[117]

Philip Strick commented in Sight & Sound, if the Wachowskis "claim no originality of message, they are startling innovators of method," praising the film's details and its "broadside of astonishing images".[118] Roger Ebert praised the film's visuals and premise, but disliked the third act's focus on action.[102] Similarly, Time Out praised the "entertainingly ingenious" switches between different realities, Hugo Weaving's "engagingly odd" performance, and the film's cinematography and production design, but concluded, "the promising premise is steadily wasted as the film turns into a fairly routine action pic ... yet another slice of overlong, high concept hokum."[119]

Jonathan Rosenbaum of the Chicago Reader reviewed the film negatively, criticizing it as "simpleminded fun for roughly the first hour, until the movie becomes overwhelmed by its many sources ... There's not much humor to keep it all life-size, and by the final stretch it's become bloated, mechanical, and tiresome."[120]

Ian Nathan of Empire described Carrie-Anne Moss as "a major find", praised the "surreal visual highs" enabled by the bullet time (or "flo-mo") effect, and described the film as "technically mind-blowing, style merged perfectly with content and just so damn cool". Nathan remarked that although the film's "looney plot" would not stand up to scrutiny, that was not a big flaw because "The Matrix is about pure experience".[121] Maitland McDonagh said in her review for TV Guide, the Wachowskis' "through-the-looking-glass plot... manages to work surprisingly well on a number of levels: as a dystopian sci-fi thriller, as a brilliant excuse for the film's lavish and hyperkinetic fight scenes, and as a pretty compelling call to the dead-above-the-eyeballs masses to unite and cast off their chains... This dazzling pop allegory is steeped in a dark, pulpy sensibility that transcends nostalgic pastiche and stands firmly on its own merits."[122]

Salon's reviewer Andrew O'Hehir acknowledged that although The Matrix is a fundamentally immature and unoriginal film ("It lacks anything like adult emotion... all this pseudo-spiritual hokum, along with the over-ramped onslaught of special effects—some of them quite amazing—will hold 14-year-old boys in rapture, not to mention those of us of all ages and genders who still harbor a 14-year-old boy somewhere inside"), but concluded, "as in Bound, there's an appealing scope and daring to The Wachowskis' work, and their eagerness for more plot twists and more crazy images becomes increasingly infectious. In a limited and profoundly geeky sense, this might be an important and generous film. The Wachowskis have little feeling for character or human interaction, but their passion for movies—for making them, watching them, inhabiting their world—is pure and deep."[97]

Filmmakers and science fiction creators alike generally took a complimentary perspective of The Matrix. William Gibson, a key figure in cyberpunk fiction, called the film "an innocent delight I hadn't felt in a long time," and stated, "Neo is my favourite-ever science fiction hero, absolutely."[123] Joss Whedon called the film "my number one" and praised its storytelling, structure and depth, concluding, "It works on whatever level you want to bring to it."[124] Darren Aronofsky commented, "I walked out of The Matrix ... and I was thinking, 'What kind of science fiction movie can people make now?' The [Wachowskis] basically took all the great sci-fi ideas of the 20th century and rolled them into a delicious pop culture sandwich that everyone on the planet devoured."[125] M. Night Shyamalan expressed admiration for The Wachowskis, stating, "Whatever you think of The Matrix, every shot is there because of the passion they have! You can see they argued it out!".[126] Simon Pegg said that The Matrix provided "the excitement and satisfaction that The Phantom Menace failed to inspire. The Matrix seemed fresh and cool and visually breathtaking; making wonderful, intelligent use of CGI to augment the on-screen action, striking a perfect balance of the real and the hyperreal. It was possibly the coolest film I had ever seen."[127] Quentin Tarantino counted The Matrix as one of his twenty favourite movies from 1992 to 2009.[128]

### Awards

The Matrix received Academy Awards for film editing, sound effects editing, visual effects, and sound. The filmmakers were competing against other films with established franchises, like Star Wars Episode I: The Phantom Menace, yet they won all four of their nominations.[129][130] The Matrix also received BAFTA awards for Best Sound and Best Achievement in Special Visual Effects, in addition to nominations in the cinematography, production design and editing categories.[131] In 1999, it won Saturn Awards for Best Science Fiction Film and Best Direction.[132]

Award Category Name Outcome
Academy Awards Best Film Editing Zach Staenberg Won
Best Sound John Reitz, Gregg Rudloff, David Campbell, David Lee Won
Best Sound Effects Editing Dane A. Davis Won
Best Visual Effects John Gaeta, Janek Sirrs, Steve Courtley, Jon Thum Won
British Academy Film Awards Best Cinematography Bill Pope Nominated
Best Editing Zach Staenberg Nominated
Best Production Design Owen Paterson Nominated
Best Sound David Lee, John Reitz, Gregg Rudloff, David Campbell, Dane A. Davis Won
Best Special Visual Effects John Gaeta, Steve Courtley, Janek Sirrs, Jon Thum Won
Saturn Awards Best Science Fiction Film Won
Best Director The Wachowski Brothers Won
Best Writer Nominated
Best Actor Keanu Reeves Nominated
Best Actress Carrie-Anne Moss Nominated
Best Supporting Actor Laurence Fishburne Nominated
Best Costumes Kym Barrett Nominated
Best Make-Up Nikki Gooley, Bob McCarron, Wendy Sainsbury Nominated
Best Special Effects John Gaeta, Janek Sirrs, Steve Courtley, Jon Thum Nominated

## Legacy

The Matrix had a strong effect on action film-making in Hollywood. The film's incorporation of wire fu techniques, including the involvement of fight choreographer Yuen Woo-ping and other personnel with a background in Hong Kong action cinema, affected the approaches to fight scenes taken by subsequent Hollywood action films,[133] moving them towards more Eastern approaches.[32] The success of The Matrix created high demand for those choreographers and their techniques from other filmmakers, who wanted fights of similar sophistication: for example, wire work was employed in X-Men (2000)[133] and Charlie's Angels (2000),[134] and Yuen Woo-ping's brother Yuen Cheung-Yan was choreographer on Daredevil (2003).[135] The Matrix's Asian approach to action scenes also created an audience for Asian action films such as Crouching Tiger, Hidden Dragon (2000) that they might not otherwise have had.[136]

Following The Matrix, films made abundant use of slow-motion, spinning cameras, and, often, the bullet time effect of a character freezing or slowing down and the camera dollying around them.[56] The ability to slow down time enough to distinguish the motion of bullets was used as a central gameplay mechanic of several video games, including Max Payne, in which the feature was explicitly referred to as "bullet time".[136][137] The Matrix's signature special effect, and other aspects of the film, have been parodied numerous times,[26] in comedy films such as Deuce Bigalow: Male Gigolo (1999),[138] Scary Movie (2000),[139] Shrek (2001),[136] Kung Pow! Enter the Fist (2002);[140] Marx Reloaded in which the relationship between Neo and Morpheus is represented as an imaginary encounter between Karl Marx and Leon Trotsky;[141] and in video games such as Conker's Bad Fur Day.[142] It also inspired films featuring a black-clad hero, a sexy yet deadly heroine, and bullets ripping slowly through the air;[26] these included Charlie's Angels (2000) featuring Cameron Diaz floating through the air while the cameras flo-mo around her; Equilibrium (2003), starring Christian Bale, whose character wore long black leather coats like Reeves' Neo;[136] Night Watch (2004), a Russian megahit heavily influenced by The Matrix and directed by Timur Bekmambetov, who later made Wanted (2008), which also features bullets ripping through air; and Inception (2010), which centers on a team of sharply dressed rogues who enter a wildly malleable alternate reality by "wiring in". The original Tron (1982) paved the way for The Matrix, and The Matrix, in turn, inspired Disney to make its own Matrix with a Tron sequel, Tron: Legacy (2010).[134]

Carrie-Anne Moss asserted that prior to being cast in The Matrix, she had "no career". It launched Moss into international recognition and transformed her career; in a New York Daily News interview, she stated, "The Matrix gave me so many opportunities. Everything I've done since then has been because of that experience. It gave me so much".[143] The film also created one of the most devoted movie fan-followings since Star Wars, and was even briefly blamed for the shootings at Columbine High School.[26] The combined success of the Matrix trilogy, the Lord of the Rings films and the Star Wars prequels made Hollywood interested in creating trilogies.[32] Stephen Dowling from the BBC noted that The Matrix's success in taking complex philosophical ideas and presenting them in ways palatable for impressionable minds might be its most influential aspect.[136]

In 2001, The Matrix placed 66th in the American Film Institute's "100 Years...100 Thrills" list.[144] In 2007, Entertainment Weekly called The Matrix the best science-fiction piece of media for the past 25 years.[15] In 2009, the film was ranked 39th on Empire's reader-, actor- and critic-voted list of "The 500 Greatest Movies of All Time".[145] The Matrix was voted as the fourth best sci-fi film in the 2011 list Best in Film: The Greatest Movies of Our Time, based on a poll conducted by ABC and People. In 2012, the film was selected for preservation in the National Film Registry by the Library of Congress for being "culturally, historically, and aesthetically significant."[16]

## Franchise

The film's mainstream success led to the making of two sequels, The Matrix Reloaded and The Matrix Revolutions, both directed by the Wachowskis. These were filmed back-to-back in one shoot and released on separate dates in 2003.[146] The first film's introductory tale is succeeded by the story of the impending attack on the human enclave of Zion by a vast machine army.[147][148] The sequels also incorporate longer and more ambitious action scenes, as well as improvements in bullet time and other visual effects.[148][149]

Also released was The Animatrix, a collection of nine animated short films, many of which were created in the same Japanese animation style[150] that was a strong influence on the live action trilogy. The Animatrix was overseen and approved by the Wachowskis, who only wrote four of the segments themselves but did not direct any of them; much of the project was developed by notable figures from the world of anime.[150]

The franchise also contains three video games: Enter the Matrix (2003), which contains footage shot specifically for the game and chronicles events taking place before and during The Matrix Reloaded;[151] The Matrix Online (2004), an MMORPG which continued the story beyond The Matrix Revolutions;[152][153] and The Matrix: Path of Neo (2005), which focuses on Neo's journey through the trilogy of films.[154]

The franchise also includes The Matrix Comics, a series of comics and short stories set in the world of The Matrix, written and illustrated by figures from the comics industry. Most of the comics were originally presented for free on the official Matrix website;[155] they were later republished, along with some new material, in two printed trade paperback volumes, called The Matrix Comics, Vol 1 and Vol 2.[156]

In March 2017, Warner Bros. was in early stages of developing a relaunch of the franchise with Zak Penn in talks to write a treatment and interest in getting Michael B. Jordan attached to star. According to The Hollywood Reporter neither the Wachowskis nor Joel Silver were involved with the endeavor, although the studio would like to get at minimum the blessing of the Wachowskis.[157]

## Home media

The Matrix was released on LaserDisc on September 21, 1999. VHS releases in both fullscreen and widescreen formats followed in December of that year. The film was released on DVD on May 15, 2007, and a Blu-ray release followed on October 14, 2008.[158] It was also released on 4K HDR Blu-ray on May 22, 2018.[159] The film as part of The Matrix Trilogy was released on 4K Ultra HD Blu-Ray on October 30, 2018.[160]

## Notes

1. ^ Credited as the Wachowski Brothers
2. ^ The film uses the word machine to describe these artificial beings but they are clearly autonomous robots with artificial intelligence (The Coming Technological Singularity: How to Survive in the Post-Human Era, by Vernor Vinge, Department of Mathematical Sciences, San Diego State University, (c) 1993 by Vernor Vinge).

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text:
Fast simulation of stabilizer circuits using a graph-state representation

@article{Anders2006FastSO,
title={Fast simulation of stabilizer circuits using a graph-state representation},
author={Simon Anders and Hans J. Briegel},
journal={Physical Review A},
year={2006},
volume={73},
pages={22334}
}
• Published 15 April 2005
• Computer Science
• Physical Review A
According to the Gottesman-Knill theorem, a class of quantum circuits\char22{}namely, the so-called stabilizer circuits\char22{}can be simulated efficiently on a classical computer. We introduce an algorithm for this task, which is based on the graph-state formalism. It shows significant improvement in comparison to an existing algorithm, given by Gottesman and Aaronson, in terms of speed and of the number of qubits the simulator can handle. We also present an implementation.
97 Citations

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These states can be regarded as an entanglement resource since one can generate a family of other multiparticle entangled states such as the generalized Greenberger-Horne-Zeilinger states of <N/2 qubits by simple measurements and classical communication.
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format: plain


text:
# Beamer document: Undefined control sequence [FIXED]

Rich Shepard rshepard at appl-ecosys.com
Fri Apr 10 15:53:16 UTC 2020

```On Fri, 10 Apr 2020, Paul A. Rubin wrote:

> I think you have a typo in the last line of your preamble, in the argument
> to \logo (should be \pdfuseimage rather than \pfuseimage)?

Paul,

Oops! That did sneak in somehow. Correcting the typo didn't fix the problem,
but I'm not using a logo in this webinar so I commented out those two lines.
That fixed the problem.

> Also, thanks for using the EastLansing theme. Go Green! Go White! Go
> State!


text:
Singular Book 2.1.6 -- matrix operations

In Macaulay2, matrices are defined over a ring. There are many ways to make a matrix, but the easiest is to use the matrix routine.
 i1 : A = QQ[x,y,z]; i2 : M = matrix{{1, x+y, z^2}, {x, 0, x*y*z}} o2 = | 1 x+y z2 | | x 0 xyz | 2 3 o2 : Matrix A <--- A i3 : N = matrix(A, {{1,2,3},{4,5,6},{7,8,9}}) o3 = | 1 2 3 | | 4 5 6 | | 7 8 9 | 3 3 o3 : Matrix A <--- A
The usual matrix arithmetic operations work.
 i4 : M+M o4 = | 2 2x+2y 2z2 | | 2x 0 2xyz | 2 3 o4 : Matrix A <--- A i5 : x*N o5 = | x 2x 3x | | 4x 5x 6x | | 7x 8x 9x | 3 3 o5 : Matrix A <--- A i6 : M*N o6 = | 7z2+4x+4y+1 8z2+5x+5y+2 9z2+6x+6y+3 | | 7xyz+x 8xyz+2x 9xyz+3x | 2 3 o6 : Matrix A <--- A i7 : N^3 o7 = | 468 576 684 | | 1062 1305 1548 | | 1656 2034 2412 | 3 3 o7 : Matrix A <--- A i8 : ((x+y+z)*N)^3 o8 = | 468x3+1404x2y+1404xy2+ | 1062x3+3186x2y+3186xy2 | 1656x3+4968x2y+4968xy2 ------------------------------------------------------------------------ 468y3+1404x2z+2808xyz+1404y2z+1404xz2+1404yz2+468z3 +1062y3+3186x2z+6372xyz+3186y2z+3186xz2+3186yz2+1062z3 +1656y3+4968x2z+9936xyz+4968y2z+4968xz2+4968yz2+1656z3 ------------------------------------------------------------------------ 576x3+1728x2y+1728xy2+576y3+1728x2z+3456xyz+1728y2z+1728xz2+1728yz2+576z 1305x3+3915x2y+3915xy2+1305y3+3915x2z+7830xyz+3915y2z+3915xz2+3915yz2+13 2034x3+6102x2y+6102xy2+2034y3+6102x2z+12204xyz+6102y2z+6102xz2+6102yz2+2 ------------------------------------------------------------------------ 3 684x3+2052x2y+2052xy2+ 05z3 1548x3+4644x2y+4644xy2 034z3 2412x3+7236x2y+7236xy2 ------------------------------------------------------------------------ 684y3+2052x2z+4104xyz+2052y2z+2052xz2+2052yz2+684z3 | +1548y3+4644x2z+9288xyz+4644y2z+4644xz2+4644yz2+1548z3 | +2412y3+7236x2z+14472xyz+7236y2z+7236xz2+7236yz2+2412z3 | 3 3 o8 : Matrix A <--- A
Indices in Macaulay2 are always 0 based, so the upper left entry is (0,0). Indexing is performed using _.
 i9 : M_(1,2) o9 = x*y*z o9 : A
Matrices cannot be modified. Make a MutableMatrix if you want to modify a matrix.
 i10 : M1 = mutableMatrix M o10 = | 1 x+y z2 | | x 0 xyz | o10 : MutableMatrix i11 : M1_(1,2) = 37_A o11 = 37 o11 : A i12 : M1 o12 = | 1 x+y z2 | | x 0 37 | o12 : MutableMatrix i13 : matrix M1 o13 = | 1 x+y z2 | | x 0 37 | 2 3 o13 : Matrix A <--- A
Matrices can be concatenated, either horizontally or vertically. The number of rows must match for horizontal concatenation, and the number of columns must match for vertical concatenation.
 i14 : M | M o14 = | 1 x+y z2 1 x+y z2 | | x 0 xyz x 0 xyz | 2 6 o14 : Matrix A <--- A i15 : M || N o15 = | 1 x+y z2 | | x 0 xyz | | 1 2 3 | | 4 5 6 | | 7 8 9 | 5 3 o15 : Matrix A <--- A
Use ideal(Matrix) to obtain the ideal generated by the entries of a matrix.
 i16 : ideal M 2 o16 = ideal (1, x, x + y, 0, z , x*y*z) o16 : Ideal of A
The $n$ by $n$ identity matrix is the identity map of the freemodule $A^n$.
 i17 : F = A^5 5 o17 = A o17 : A-module, free i18 : id_(A^5) o18 = | 1 0 0 0 0 | | 0 1 0 0 0 | | 0 0 1 0 0 | | 0 0 0 1 0 | | 0 0 0 0 1 | 5 5 o18 : Matrix A <--- A
In Macaulay2, integer matrices are just matrices defined over the ring of integers ZZ.
 i19 : matrix{{1,2,3},{4,5,6}} o19 = | 1 2 3 | | 4 5 6 | 2 3 o19 : Matrix ZZ <--- ZZ


text:
# Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Definition 9.5.0.37. Let $\operatorname{\mathcal{QC}}$ denote the $\infty$-category of small $\infty$-categories (Construction 5.6.4.1), and let $\operatorname{\mathcal{Q}}\subseteq \operatorname{\mathcal{QC}}$ be a full subcategory. We will say that a cocartesian fibration $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ is $\operatorname{\mathcal{Q}}$-small if, for every object $C \in \operatorname{\mathcal{D}}$, the fiber $\operatorname{\mathcal{E}}_{C} = \{ C \} \times _{\operatorname{\mathcal{C}}} \operatorname{\mathcal{E}}$ is equivalent to an $\infty$-category which belongs to $\operatorname{\mathcal{Q}}$.


text:
# The inside perimeter of a running track (shown in the following figure) is 400 m.

Question:

The inside perimeter of a running track (shown in the following figure) is 400 m. The length of each of the straight portion is 90 m and the ends are semi-circles. If the track is everywhere 14 m wide. find the area of the track. Also find the length of the outer running track.

Solution:

It is given that, length of each straight portion $=90 \mathrm{~m}$ and width of track $=14 \mathrm{~m}$

We know that the circumference C of semicircle of radius be r is

$C=\pi r$

The inside perimeter of running track is the sum of twice the length of straight portion and circumferences of semicircles. So,
inside perimeter of running track = 400 m

$2 l+2 \pi r=400 m$

$\Rightarrow 2 \times 90+2 \times \frac{22}{7} \times r=400 m$

$\Rightarrow r=\frac{220 \times 7}{2 \times 22}=35 \mathrm{~m}$

Thus, radius of inner semicircle is 35 m.

Now,

radius of outer semi circle r' = 35 + 14 = 49 m

Area of running track $=2 \times$ Area of rectangle $+2 \times$ Area of outer semi circle $-2 \times$ Area of inner semicircle

$=2 \times 90 \times 14+2 \times \frac{\pi(49)^{2}}{2}-2 \times \frac{\pi(35)^{2}}{2}$

$=2520+\pi \times(49+35)^{2}(49-35)$

$=2520+\frac{22}{7} \times 84 \times 14$

$=2520+3696=6216 m^{2}$

Hence, the area of running track $=6216 \mathrm{~m}^{2}$

Now, length L of outer running track is

$\mathrm{L}=2 \times 1+2 \pi r^{\prime}$

$=2 \times 90+2 \pi \times 49$

$=180+2 \times \frac{22}{7} \times 49$

$=180+308=488 m$

Hence, the length L of outer running track is 488 m.


text:
# $p$-Valent strongly starlike and strongly convex functions connected with linear differential Borel operator

Volume 26, Issue 2, pp 137--148
Publication Date: November 05, 2021 Submission Date: July 30, 2021 Revision Date: September 02, 2021 Accteptance Date: September 17, 2021
• 163 Views

### Authors

S. M. El-Deeb - Department of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, Egypt. - Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 51452, Saudi Arabia. G. Murugusundaramoorthy - Department of Mathematics, School of Advanced Sciences, Vellore Institute Technology University, Vellore - 632014, India. A. Alburaikan - Department of Mathematics, College of Science and Arts, Al-Badaya, Qassim University, Buraidah 51452, Saudi Arabia.

### Abstract

In this paper, we define two subclasses $\mathcal{S}^{\ast }\left( \alpha ,m,\delta ,p,q,\lambda ,\gamma ,\beta \right)$ and $\mathcal{K}\left( \alpha ,m,\delta ,p,q,\lambda ,\gamma ,\beta \right)$ of strongly starlike and strongly convex functions of order $\beta$ and type $\gamma \$by using the linear $q$-differential Borel operator. We also derive some interesting properties, such as inclusion relationships of these classes and the integral operator $\mathcal{J}_{\mu ,p}$.

### Share and Cite

##### ISRP Style

S. M. El-Deeb, G. Murugusundaramoorthy, A. Alburaikan, $p$-Valent strongly starlike and strongly convex functions connected with linear differential Borel operator, Journal of Mathematics and Computer Science, 26 (2022), no. 2, 137--148

##### AMA Style

El-Deeb S. M., Murugusundaramoorthy G., Alburaikan A., $p$-Valent strongly starlike and strongly convex functions connected with linear differential Borel operator. J Math Comput SCI-JM. (2022); 26(2):137--148

##### Chicago/Turabian Style

El-Deeb, S. M., Murugusundaramoorthy, G., Alburaikan, A.. "$p$-Valent strongly starlike and strongly convex functions connected with linear differential Borel operator." Journal of Mathematics and Computer Science, 26, no. 2 (2022): 137--148

### Keywords

• $p$-Valent
• strongly starlike
• strongly convex
• linear $q$-differential Borel operator

•  05A30
•  30C45
•  11B65
•  47B38

### References

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• [2] M. K. Aouf, S. M. El-Deeb, On $p$-valent strongly starlike and strongly convex functions assoicated with generalized linear operator, Montes Taurus J. Pure Appl. Math., 3 (2021), 104--111

• [3] M. K. Aouf, H. M. Hossen, New criteria for meromorphic $p$-valent starlike functions, Tsukuba J. Math., 17 (1993), 481--486

• [4] J. H. Choi, M. Saigo, H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 276 (2002), 432--445

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