Singular value inequalities with applications
Volume 24, Issue 4, pp 323--329
http://dx.doi.org/10.22436/jmcs.024.04.04
Publication Date: April 08, 2021
Submission Date: January 21, 2021
Revision Date: February 18, 2021
Accteptance Date: March 18, 2021
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Authors
Wasim Audeh
- Department of Mathematics, University of Petra, Amman, Jordan.
Abstract
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.
Share and Cite
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
Keywords
- Singular value
- convex function
- positive operator
- inequality
MSC
- 15A18
- 15A42
- 15A60
- 47A63
- 47B05
- 47B15
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