Two inequalities involving Hadamard products of positive semi-definite Hermitian matrices

Authors:
Chong-Guang Cao;Zhong-Peng Yang;Xian Zhang
Affiliations:
Department of Mathematics, Heilongjiang Univ., Harbin, P. R. China;School of Mechanical and Manufacturing Engineering, The Queen's University of Belfast, Stranmillis Road, Belfast, UK;Department of Mathematics, Heilongjiang Univ., Harbin, P. R. China
Venue:
The Korean Journal of Computational & Applied Mathematics
Year:
2002

Citing 3
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Matrix analysis

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Abstract

We extend two inequalities involving Hadamard products of positive definite Hermitian matrices to positive semi-definite Hermitian matrices. Simultaneously, we also show the sufficient conditions for equalities to hold. Moreover, some other matrix inequalities are also obtained. Our results and methods are different from those which are obtained by S. Liu in [J. Math. Anal. Appl. 243:458-463(2000)] and B.-Y. Wang et al in [Lin. Alg. Appl. 302-303:163-172(1999)].