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Some inequalities for singular values and eigenvalues of generalized Schur complements of products of matrices

โœ Scribed by Jianzhou Liu

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
717 KB
Volume
286
Category
Article
ISSN
0024-3795

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โœฆ Synopsis

is paper, using tra~sfo~atio~ of Schr estimates of eigenvnlues of positive se~~i~efiuite ualities of singular values for Schur co tian matrices we Kevwor&~ . .

๐Ÿ“œ SIMILAR VOLUMES

Some inequalities for singular values of
Some inequalities for singular values of matrix products
โœ Bo-Ying Wang; Bo-Yan Xi ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 213 KB

Let crl(C) >/ ... /> cr,(C) denote the singular values of a matrix C ~ C "xm, and let 1 ~1 k o. r A r k r r ~t=l i,( )orn\\_t+l(B) and ~.kt=lo'tr(AB) ~ Et=lo'~(A)tr,\\_i,+l(B), where A C pร—", B ~ C nxm. We also consider the cases for the product of three matrices and more.

A minimum principle and estimates of the
A minimum principle and estimates of the eigenvalues for schur complements positive semidefinite hermitian matrices
โœ Jianzhou Liu; Li Zhu ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 536 KB

We give a minimum principle for Sehur complements of positive definite Herrnitian matrices. Further, we obtain some inequalities for the eigenvalues of Schur complements of products and sums of positive definite Hermitian matrices.

Some inequalities for sum and product of
Some inequalities for sum and product of positive semidefinite matrices
โœ Bo-Ying Wang; Bo-Yan Xi; Fuzhen Zhang ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 101 KB

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.