@article { author = {Sheikhhosseini, Alemeh and Aghamollaei, Golamreza}, title = {Cartesian decomposition of matrices and some norm inequalities}, journal = {Wavelet and Linear Algebra}, volume = {3}, number = {2}, pages = {33-42}, year = {2016}, publisher = {Vali-e-Asr university of Rafsanjan}, issn = {2383-1936}, eissn = {2476-3926}, doi = {10.22072/wala.2016.23238}, 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.}, keywords = {‎joint C-numerical radius‎,‎C-spectral norm‎,‎joint spectral radius}, url = {https://wala.vru.ac.ir/article_23238.html}, eprint = {https://wala.vru.ac.ir/article_23238_64b86b56682082a7a0b0f1d249c90a93.pdf} }