In this work, we investigate inequalities of singular values and unitarily invariant norms for sums products matrices. First, give an another more concise clear proof to inequality obtained by Chen Zhang [6, Theorem 5]. Then, establish values. addition, also a As applications inequality, present some inequalities.

Whenever we have a group acting on a class of functions by translation, the bispectrum offers a principled and lossless way of representing such functions invariant to the action. Unfortunately, computing the bispectrum is often costly and complicated. In this paper we propose a unitarily equivalent, but easier to compute set of invariants, which we call the skew spectrum. For functions on homo...

Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard–Stratonovich transformation. Here, we complete this extension by including arbitrary orthogonally and unitary–symplectically invariant matrix ensembles. The results are equivalent to, but the approach is different from the superbosonization formul...

Sufficient conditions are established in order that, for a fixed infinite set of sampling points on the full line, a function satisfies a sampling theorem on a suitable closed subspace of a unitarily translation invariant reproducing kernel Hilbert space. A number of examples of such reproducing kernel Hilbert spaces and the corresponding sampling expansions are given. Sampling theorems for fun...

Within the latent growth curve model, time-invariant covariates are generally modeled on the subject level, thereby estimating the effect of the covariate on the latent growth parameters. Incorporating the time-invariant covariate in this manner may have some advantages regarding the interpretation of the effect but may also be incorrect in certain instances. In this article we discuss a more g...

We study multiplicative statistics for the eigenvalues of unitarily-invariant Hermitian random matrix models. consider one-cut regular polynomial potentials and a large class statistics. show that in limit several associated quantities converge to limits which are universal both potential family considered. In turn, such described by integro-differential Painlev\'e II equation, particular they ...