Combined Matrix of a Tridiagonal Toeplitz Matrix

[EN] In this work, combined matrices of tridiagonal Toeplitz matrices are studied. The combined matrix is known as the Relative Gain Array in control theory. In particular, given a real tridiagonal Toeplitz matrix of order n, the characterization of its combined matrix as a bisymmetric and doubly qu...

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Bibliographic Details
Authors: Cantó Colomina, Begoña|||0000-0002-9837-3926, Cantó Colomina, Rafael|||0000-0002-1341-2800, Urbano Salvador, Ana María|||0000-0001-8590-1243
Format: article
Publication Date:2025
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/223570
Online Access:https://riunet.upv.es/handle/10251/223570
Access Level:Open access
Keyword:Tridiagonal Toeplitz matrix
Combined matrix
Doubly quasi-stochastic matrix
Jacobi matrix
Linear algebra
Description
Summary:[EN] In this work, combined matrices of tridiagonal Toeplitz matrices are studied. The combined matrix is known as the Relative Gain Array in control theory. In particular, given a real tridiagonal Toeplitz matrix of order n, the characterization of its combined matrix as a bisymmetric and doubly quasi-stochastic matrix is studied. Furthermore, this paper addresses the inverse problem, that is, given a bisymmetric, doubly quasi-stochastic tridiagonal Jacobi matrix U of order n, determine under what conditions there exists a real tridiagonal Toeplitz matrix A such that its combined matrix is U.