More results on singular value inequalities of matrices
By Y. Tao. 2006
70 citations recorded by the source corpus.
Abstract The arithmetic–geometric mean inequality for singular values due to Bhatia and Kittaneh says that 2 s j ( AB ∗ ) ⩽ s j ( 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 that s j A 1 4 B 3 4 + A 3 4 B 1 4 ⩽ s j ( A + B ) , j = 1 , … , n for any n × n positive semidefinite matrices A, B, which proves a special case of Zhan’s conjecture posed in 2000.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/8eb7a7144a2ba0cfa4e35dbc28adb9ae0ae2bd89
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Singular value inequalities for compact operators (2012, background): “Moreover, Tao has proved in [7] that if A, B, C ∈ K(H) such that ⎡ ⎣ A B B∗ C ⎤ ⎦ 0, then”