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Inequalities for a Complex Matrix Whose Real Part is Positive Definite

1975
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Transactions of the American Mathematical Society
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Denote the real part of A e Ai"(C) by H(A) = Vi(A + A*). We provide dual inequalities relating H(A~ ) and H(A)~ and an identity between two functions of A when A satisfies H(A) > 0. As an application we give an inequality (for matrices A satisfying H(A) > 0) which generalizes Hadamard's determinantal inequality for positive definite matrices. 0. Introduction. Denote the real part of an n by n complex matrix A by HiA) = %A +A*) and define II" = {A G MniC): HiA) > 0}. If A G l\n, then A is

doi:10.2307/1998618
fatcat:afv3qdwmvzhxni2yzvh4wepcde