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Some inequalities for sum and product of positive semidefinite matrices

โœ Scribed by Bo-Ying Wang; Bo-Yan Xi; Fuzhen Zhang

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
101 KB
Volume
293
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

The purpose of this paper is to present some inequalities on majorization, unitarily invariant norm, trace, and eigenvalue for sum and product of positive semideยฎnite (Hermitian) matrices. Some open questions proposed by Marshall and Olkin are resolved.

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The main result of this paper is the following: if both A = (a ij ) and B = (b ij ) are Mmatrices or positive definite real symmetric matrices of order n, the Hadamard product of A and B is denoted by A โ€ข B, and A k and B k (k = 1, 2, . . . , n) are the k ร— k leading principal submatrices of A and B