Departamento de Matemática Aplicada, Universitat Politècnica de València, Valencia, Spain. It is well known that for a family of orthogonal polynomials the so-called “generating functions” ...

In this comment we will demonstrate that one of the main formulas given in Ref. [1] is incorrect. 1. Introduction and Motivation It is well known that for a family of orthogonal polynomials the ...

Any nonsingular function of spin j matrices always reduces to a matrix polynomial of order 2j. The challenge is to find a convenient form for the coefficients of the matrix polynomial. The theory of ...

The exponential of an N × N matrix can always be expressed as a matrix polynomial of order N − 1. In particular, a general group element for the fundamental representation of SU(N) can be expressed as ...

Invariant polynomials with matrix arguments have been defined by the theory of group representations, generalizing the zonal polynomials. They have developed as a useful tool to evaluate certain ...

Abstract: The matrix-valued spherical functions for the pair (K×K,K), K=SU(2), are studied. By restriction to the subgroup A, the matrix-valued spherical functions are diagonal. For suitable set of ...

Three modes of operation are supported. The first takes a polynomial and a given size of matrix, then evaluates if that polynomial probably preserves the nonnegativity of those matrices. The second is ...

Departamento de Física Teórica II (Métodos Matemáticos de la Física), Universidad Complutense de Madrid, Ciudad Universitaria, Plaza de Ciencias 1, 28040 Madrid, Spain ...

Abstract: This paper considers interpolating matrix polynomials P(λ) in Lagrange and Hermite bases. A classical approach to investigating the polynomial eigenvalue problem P(λ) x = 0 is linearization, ...

The polynomial eigenvalue problem is to find the eigenpair of $(\lambda,x) \in \mathbb{C}\bigcup \{\infty\} \times \mathbb{C}^n \backslash \{0\}\(that satisfies \)P ...

Hello everyone, I want to calculate the determinant of some specific matrix. I have simplified my problem and try to demonstrate the problem with the simplest code below. I suspect that it should be ...