Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions (Q1103024)
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scientific article; zbMATH DE number 4051807
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions |
scientific article; zbMATH DE number 4051807 |
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Complementary triangular forms of pairs of matrices, realizations with prescribed main matrices, and complete factorization of rational matrix functions (English)
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1988
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By definition, \(m\times m\) matrices A and Z admit simultaneous reduction to complementary triangular forms if there exists an invertible \(m\times m\) matrix S such that \(S^{-1}AS\) is an upper triangular matrix and \(S^{-1}ZS\) is a lower triangular matrix. Several sufficient conditions for such an S to exist are given. There is a connection with the problem of complete factorization of a transfer function.
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minimal factorization
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simultaneous reduction
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complementary triangular forms
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triangular matrix
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complete factorization
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transfer function
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