Fr.: espace euclidean
A space in which the → distance between any two points is given by the → Pythagorean theorem: d2 = (Δx)2 + (Δy)2 + (Δz)2, where d is distance and Δx, Δy, and Δz are differential → Cartesian coordinates. Euclidean n-space Rn is the set of all column vectors with n real entries.
Fr.: espace pseudo-euclidien
A real vector space of dimension n having a symmetric bilinear form (x, y) such that in some basis e1, ..., en, the quadratic form (x2) takes the form x12 + ... + xn - 12 - xn2. Such bases are called orthonormal.