Combined Matrix of a Tridiagonal Toeplitz Matrix

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 <i>n</i>, the characterization of its combined matrix as a bisymmetric...

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Bibliographic Details
Main Authors: Begoña Cantó, Rafael Cantó, Ana Maria Urbano
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/14/5/375
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Summary: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 <i>n</i>, 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 <i>U</i> of order <i>n</i>, determine under what conditions there exists a real tridiagonal Toeplitz matrix <i>A</i> such that its combined matrix is <i>U</i>.
ISSN:2075-1680