Inequalities for generalized matrix function and inner product

Abstract

We present inequalities related to generalized matrix function for positive semidefinite block matrices. We introduce partial generalized matrix functions corresponding to partial traces, and then provide a unified extension of the recent inequalities due to Lin [Electron. J. Linear Algebra 27 (2014) 821-826], Zhang et al. [Linear Algebra Appl. 498 (2016) 99-105] and [Electron. J. Linear Algebra 27 (2014) 332-341] and a result of Choi [Linear Algebra Appl. 532 (2017) 1-7]. Moreover, we demonstrate the application of a positive semidefinite $3\times 3$ block matrix, which motivates us to give alternative proofs of Dragomir's inequality and Krein's inequality.

14 pages. Any comments are welcome. E-mail address: [email protected]

References in corpus (1)

• Advances on Inequalities of the Schwarz, Triangle and Heisenberg Type in Inner Product Spaces