Inequalities for a Complex Matrix Whose Real Part is Positive Definite

Charles R. Johnson
1975 Transactions of the American Mathematical Society  
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
more » ... n, then A is nonsingular and Received by the editors July 2, 1974. AMS (MOS) subject classifications (1970). Primary 15A09, 15A45, 15A57.
doi:10.2307/1998618 fatcat:afv3qdwmvzhxni2yzvh4wepcde