Inequalities for a complex matrix whose real part is positive definite

Johnson, Charles R.

doi:10.1090/S0002-9947-1975-0424851-2

Inequalities for a complex matrix whose real part is positive definite
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by Charles R. Johnson PDF

Trans. Amer. Math. Soc. 212 (1975), 149-154 Request permission

Abstract:

Denote the real part of $A \in {M_n}(C)$ by $H(A) = 1/2(A + {A^\ast })$. We provide dual inequalities relating $H({A^{ - 1}})$ and $H{(A)^{ - 1}}$ 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.

References

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