An eigenvalue inequality for positive semidefinite k × k block matrices

An Eigenvalue Majorization Inequality for Positive Semidefinite Block Matrices: In Memory of Ky Fan

2 Let H = [ M K K∗ N ] be a Hermitian matrix. It is known that the eigenvalues of M ⊕N are 3 majorized by the eigenvalues of H . If, in addition, H is positive semidefinite and the block K 4 is Hermitian, then the following reverse majorization inequality holds for the eigenvalues: 5

A Norm Compression Inequality for Block Partitioned Positive Semidefinite Matrices

where B and D are square blocks. We prove the following inequalities for the Schatten q-norm ||.||q , which are sharp when the blocks are of size at least 2× 2: ||A||q ≤ (2 q − 2)||C||q + ||B|| q q + ||D|| q q, 1 ≤ q ≤ 2, and ||A||q ≥ (2 q − 2)||C||q + ||B|| q q + ||D|| q q, 2 ≤ q. These bounds can be extended to symmetric partitionings into larger numbers of blocks, at the expense of no longer...

A determinantal inequality for positive semidefinite matrices

Let A,B,C be n× n positive semidefinite matrices. It is known that det(A+ B + C) + detC ≥ det(A+ C) + det(B + C), which includes det(A+B) ≥ detA+ detB as a special case. In this article, a relation between these two inequalities is proved, namely, det(A+ B + C) + detC − (det(A+ C) + det(B + C)) ≥ det(A+ B)− (detA+ detB).

Singular value inequalities for positive semidefinite matrices

In this note‎, ‎we obtain some singular values inequalities for positive semidefinite matrices by using block matrix technique‎. ‎Our results are similar to some inequalities shown by Bhatia and Kittaneh in [Linear Algebra Appl‎. ‎308 (2000) 203-211] and [Linear Algebra Appl‎. ‎428 (2008) 2177-2191]‎.

A norm inequality for pairs of commuting positive semidefinite matrices