S-matrices (Q794744)
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scientific article; zbMATH DE number 3859322
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | S-matrices |
scientific article; zbMATH DE number 3859322 |
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S-matrices (English)
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1984
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Given a complex matrix A consider the matrix B obtained from A by adding a column consisting of \(1,x,x^ 2,..\). where x is an indeterminate. Let r be the rank of A. The matrix A is said to be an S-matrix if the gcd of all subdeterminants of B of order \(r+1\) is a polynomial of degree r. Existence and uniqueness of a decomposition of an S-matrix into a quasidirect sum of indecomposable summands is proved. Connections with Vandermonde matrices, Hankel matrices, infinite companion matrices [cf. the reviewer, ibid. 1, 245-260 (1968; Zbl 0159.323) and ibid. 49, 57-78 (1983; Zbl 0506.15015)] are pointed out.
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S-matrix
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decomposition
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quasidirect sum
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indecomposable summands
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Vandermonde matrices
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Hankel matrices
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infinite companion matrices
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0.8965045
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