Canonical Positive Definite Matrices Under Internal Linear Transformations

Bernard Vinograde
1950 Proceedings of the American Mathematical Society  
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
more » ... parts is for convenience only.
doi:10.2307/2031917 fatcat:kij7qwhu3zfjvgiznvw7xftrlq