ILAS2016 — 11–15 July 2016 — KU Leuven, Belgium

## 20th ILAS Conference

Contributed talks on Block Orthogonalization

Mon 14:30–15:00, Room AV 00.17, Chair: Jesse L. Barlow
Inequalities for the powers of positive semidefinite block matrices
Zübeyde Ulukök (Selcuk University)

Let $H = \left[ {\begin{array}{*{20}{c}}M&K\\{{K^ * }}&N \end{array}} \right]$ be a positive semidefinite block matrix with square matrices $M$ and $N$ of the same order. In this talk, we present inequalities which produce eigenvalue and unitarily invariant norm inequalities, for the powers of $H$. Then under the additional assumptions that $K$ is Hermitian or skew-Hermitian, we give the special cases of the obtained inequality. Furthermore, we are interested in the majorization inequalities for the eigenvalues of $H$.