The matrix obtained from a given (rectangular or square) matrix (; ) by interchanging the rows and the columns, that is, the matrix , where (; ). The number of rows of the transposed matrix is equal to the number of columns of , while the number of columns is equal to the number of rows of . The transpose of a matrix is usually denoted by or .
Some elementary properties of the transposition of matrices are , , , .
|[a1]||F.R. [F.R. Gantmakher] Gantmacher, "The theory of matrices" , 1 , Chelsea, reprint (1959) pp. 19 (Translated from Russian)|
Transposed matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transposed_matrix&oldid=15848