Canonical positive definite matrices under internal linear transformations
Bernard Vinograde · Proceedings of the American Mathematical Society · 1950
Let P be a real positive definite n-rowed square matrix, n = p+q +r, p^qg,r, S = diag (Si, S2, S3), where Si is p-rowed, 52 is g-rowed, and S3 is r-rowed, all nonsingular.S is called an internal linear transformation when it transforms P according to the rule P^SPS'.All coefficients are real numbers.The problem is to find a canonical form for P, under internal linear transformations, depending on characteristic value systems associated with P. The partition of n into three parts is for convenience only.