Elementary bidiagonal factorizations (Q1124871)
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scientific article; zbMATH DE number 1371374
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Elementary bidiagonal factorizations |
scientific article; zbMATH DE number 1371374 |
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Elementary bidiagonal factorizations (English)
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29 November 1999
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An elementary bidiagonal matrix is a square matrix such that every entry in the diagonal is \(1,\) exactly one entry either on the sub- or superdiagonal is nonzero, and all other entries are zero. The authors show that every \(n\times n\) matrix is a product of elementary bidiagonal matrices. For special cases, e.g., for \(2\times 2\) and \(3\times 3\) matrices they also determine the minimal number of factors needed in any elementary bidiagonal factorization.
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elementary bidiagonal matrix
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factorization
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triangular matrix
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product
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