We study the empirical spectral distribution (ESD) for complex [Formula: see text] matrix polynomials of degree under relatively mild assumptions on underlying distributions, thus highlighting universality phenomena. In particular, we assume that entries each coefficient polynomial have mean zero and finite variance, potentially allowing distinct distributions coefficients. derive almost sure l...

The paper reports a method for compressed representation of matrix data on the principles quantum theory. is formalized as complex-valued factorization based standard singular value decomposition. developed approach establishes bridge between methods semantic analysis and models cognition decision. According to theory, real-valued observable quantities are generated by wavefunctions being vecto...

Definitions. a) A matrix is called a complex matrix if all its entries are complex numbers. (In particular, any vector in C is considered a n× 1 complex matrix.) b) For any complex matrix A, we denote the matrix A T by A∗. c) Let U2 (C) be the group of all unitary 2× 2 complex matrices. In other words, let U2 (C) = { U ∈ GL2 (C) | U∗ = U−1 } . d) A complex matrix A is called Hermitian if it sat...

mn(ii) salen complex immobilized on nano silicagel was prepared by incorporating mn(ii) salen complex into a nanosilica matrix and characterized by tga, xrd, atomic absorption spectroscopy and was successfully applied as catalyst for the oxidation of alcohols. oxidation of a series of alcohols in acetonitrile over immobilized mn(ii) salen complex using tetrabutylammonium peroxymonosulfate (tbao...