Let "A" be a symmetric square matrix of order "n" with real entries. Any non-singular matrix "S" of the same size is said to transform "A" into another symmetric matrix , also of order "n", where "S"T is the transpose of "S". It is also said that matrices "A" and "B" are congruent. If "A" is the coefficient matrix of some quadratic form of R"n", then "B" is the matrix for the same form after the change of basis defined by "S".