‎This paper presents two main results that the singular values of the Hadamard product of normal matrices $A_i$ are weakly log-majorized by the singular values of the Hadamard product of $|A_{i}|$ and the singular values of the sum of normal matrices $A_i$ are weakly log-majorized by the singular values of the sum of $|A_{i}|$‎. ‎Some applications to these inequalities are also given‎. ‎In addi...

2 Preliminaries 7 2.1 Matrices and their singular values . . . . . . . . . . . . . . . . . . 7 2.2 Nets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Sub-gaussian random variables . . . . . . . . . . . . . . . . . . . 9 2.4 Sub-exponential random variables . . . . . . . . . . . . . . . . . . 14 2.5 Isotropic random vectors . . . . . . . . . . . . . . . . . . . . . . ...

— Multi-Input Multi-Output (MIMO) transmission has been a topic of great interest for a few years due to the huge spectral ef ciency gain it can provide over rich scattering transmission channels, such as indoor (e.g. wireless local area networks) or urban outdoor (e.g. mobile wireless communications). MIMO transmission channels are usually modelled by random matrices. In this paper, we use res...

The article ”Random matrix theory in statistics: A review” was written by D. Paul and A. Aue and published in the Journal of Statistical Planning and Inference in 2015. Random Matrix Theory (RMT) is interested among other topics in describing the asymptotic behavior of the singular values and singular vectors of random matrices. Random matrices emerge in many statistical problems, that can be t...