%0 Journal Article %T Singular value inequalities with applications %A Audeh, Wasim %J Journal of Mathematics and Computer Science %D 2022 %V 24 %N 4 %@ ISSN 2008-949X %F Audeh2022 %X 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. %9 journal article %R 10.22436/jmcs.024.04.04 %U http://dx.doi.org/10.22436/jmcs.024.04.04 %P 323--329