Singular value inequalities with applications

Volume 24, Issue 4, pp 323--329
Publication Date: April 08, 2021 Submission Date: January 21, 2021 Revision Date: February 18, 2021 Accteptance Date: March 18, 2021


Wasim Audeh - Department of Mathematics, University of Petra, Amman, Jordan.


Let \(A_{i},B_{i},X_{i},Y_{i}\) be \(n\times n\) complex matrices, \(i=1,2,...,m\) and let \(f\) be a nonnegative increasing convex function on an interval \(I\) such that \(0\in I\) and \(f(0)\leq 0\). Then% \[ 2s_{j}\left( f\left( \left \vert \sum \limits_{i=1}^{m}A_{i}X_{i}Y_{i}^{\ast }B_{i}^{\ast }\right \vert \right) \right) \leq \left( \max \left \{ S,T\right \} \right) ^{2}s_{j}(K) \] for $j=1,2,...,n,$ where% \[ S=\left \Vert \sum \limits_{i=1}^{m}A_{i}A_{i}^{\ast }\right \Vert ^{1/2}\text{% , }T=\left \Vert \sum \limits_{i=1}^{m}B_{i}B_{i}^{\ast }\right \Vert ^{1/2}% \text{,} \] \[ K=f(\left \vert X_{1}\right \vert ^{2}+\left \vert Y_{1}\right \vert ^{2})\oplus ...\oplus f(\left \vert X_{m}\right \vert ^{2}+\left \vert Y_{m}\right \vert ^{2}) \] and \(\max \left \{ S,T\right \} \leq 1\). Several singular value inequalities are also proved.

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ISRP Style

Wasim Audeh, Singular value inequalities with applications, Journal of Mathematics and Computer Science, 24 (2022), no. 4, 323--329

AMA Style

Audeh Wasim, Singular value inequalities with applications. J Math Comput SCI-JM. (2022); 24(4):323--329

Chicago/Turabian Style

Audeh, Wasim. "Singular value inequalities with applications." Journal of Mathematics and Computer Science, 24, no. 4 (2022): 323--329