An algorithmic approach to simultaneous triangularization (Q1020928)
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scientific article; zbMATH DE number 5561705
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An algorithmic approach to simultaneous triangularization |
scientific article; zbMATH DE number 5561705 |
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An algorithmic approach to simultaneous triangularization (English)
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4 June 2009
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The problem of determining whether or not a set of matrices, denoted by \(S\), admits a simultaneous triangularization is a long studied problem. This paper presents an algorithm to solve this problem. In order to apply this algorithm, one must have an algorithm for computing a common eigenvector for a set of matrices. To this end, one can run the \textit{D. Shemesh} algorithm [Linear Algebra Appl. 62, 11--18 (1984; Zbl 0556.15006)] for all pairs of matrices in \(S\) and bisect the results.
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simultaneous triangularization
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Lie algebra
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common eigenvector
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Shemesh algorithm
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