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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
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| Series: | Axioms |
| Subjects: | |
| 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>. |
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| ISSN: | 2075-1680 |