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Canonical Positive Definite Matrices Under Internal Linear Transformations

1950
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Proceedings of the American Mathematical Society
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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

doi:10.2307/2031917
fatcat:kij7qwhu3zfjvgiznvw7xftrlq