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)].
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Partially supported by the N. S. F. of Heilongjiang province under grant No. A01-07, and the N. S. F. of Heilongjiang Education Committee under grant No. 15011014.
Partially supported by NSF of Fujian Education Committee.
Chong-guang Cao received his MS from Northeastern Normal University. Since 1981 he has been at the Heilongjiang University. In 1992, he received a Professor from Heilongjiang Education Committee. His research interests center on the theory of classical group and matrix algebra.
Zhong-peng Yang was graduated from Jinlin Teachers College. Since 1979 he has been at Jinlin Teachers College, which named him an Professor in 1998. In 2000, he has been at Putian College. His research interests center on the theory of matrix algebra and its applications.
Xian Zhang received his BS from Heilongjiang University. Since 1990 he has been at the Heilongjiang University, which named him an Assistant in 1994. In September of 2001, he received a Assistant Professor from Heilongjiang Education Committee. In November of 2001, he come to UK for his Ph. D., degree. His research interests center on the theory of matrix algebra, the theory of linear control, and theirs applications.
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Cao, CG., Yang, ZP. & Zhang, X. Two inequalities involving Hadamard products of positive semi-definite Hermitian matrices. JAMC 10, 101–109 (2002). https://doi.org/10.1007/BF02936209
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DOI: https://doi.org/10.1007/BF02936209