Author = Sheikhhosseini, Alemeh
Number of Articles: 1
Cartesian decomposition of matrices and some norm inequalities
Volume 3, Issue 2, 2016, Pages 33-42
https://doi.org/10.22072/wala.2016.23238
Alemeh Sheikhhosseini, Golamreza Aghamollaei
Abstract Let X be an n-square complex matrix with the Cartesian decomposition X = A + i B, where A and B are n times n Hermitian matrices. It is known that $Vert X Vert_p^2 leq 2(Vert A Vert_p^2 + Vert B Vert_p^2)$, where $p geq 2$ and $Vert . Vert_p$ is the Schatten p-norm. In this paper, this inequality and some of its improvements are studied and investigated for the joint C-numerical radius, joint spectral radius, and for the C-spectral norm of matrices.