Algebraic Aspects of combined matrices

2022/02/14 by Primitivo B. Acosta-Humánez, Acosta-Humánez, Primitivo B., Leonardo, Randy +1
Engineering · Mathematics · #(Primary) 15A18 (Secondary) 05E99 #Advanced Topics in Algebra #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2202.06848

openalex publication_date 2022/02/14 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

In this work, we present algebraic results concerning the combined matrices C(A), where the entries of A belong to a number field K and A is a non-singular matrix. In other words, A is a n× n matrix belonging to the General Linear Group over K, denoted by GL_n(K). We also analyze the case in which matrix A belongs to algebraic subgroups of GL_n(K), such as the unimodular group, where A² is a n× n matrix belonging to the Special Linear Group, denoted by SL_n(K), triangular groups, diagonal groups, among others. In particular, we thouroughly examine the cases n=2 and n=3 for symmetric and non-symmetric matrices, providing explicit diagonalization of C(A), which includes characteristic polynomials with their eigenvalues and eigenfactors.

Related

• Decomposition of matrices from SL_ 2(K[x, y])
• On sums and products of diagonalizable matrices over division rings
• Matrix symmetric and quasi-symmetric functions and noncommutative representation theory
• Representations of monomial matrices and restriction from GL_n to S_n
• Factorization in SL_n(R) with elementary matrices when R is the disk algebra and the Wiener algebra