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More results on singular value inequalities of matrices

2006; Elsevier BV; Volume: 416; Issue: 2-3 Linguagem: Inglês

10.1016/j.laa.2005.12.017

1873-1856

Yunxing Tao,

Functional Equations Stability Results

The arithmetic–geometric mean inequality for singular values due to Bhatia and Kittaneh says that2sj(AB∗)⩽sj(A∗A+B∗B),j=1,2,…for any matrices A, B. We give a new equivalent form and some relevant generalizations of this inequality. In particular, we show thatsjA14B34+A34B14⩽sj(A+B),j=1,…,nfor any n × n positive semidefinite matrices A, B, which proves a special case of Zhan's conjecture posed in 2000.