Length Function and Simultaneous Triangularization of Matrix Pairs

The paper interrelates the simultaneous triangularization problem for matrix pairs with the Paz problem and known results on the length of the matrix algebra. The length function is applied to the Al’pin–Koreshkov algorithm, and it is demonstrated how its multiplicative complexity can be reduced. An...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2023-05, Vol.272 (4), p.566-573
Main Author: Markova, O. V.
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Complexity
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrices (mathematics)
Matrix algebra
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Summary:The paper interrelates the simultaneous triangularization problem for matrix pairs with the Paz problem and known results on the length of the matrix algebra. The length function is applied to the Al’pin–Koreshkov algorithm, and it is demonstrated how its multiplicative complexity can be reduced. An asymptotically superior procedure for verifying the simultaneous triangularizability of a pair of complex matrices is provided. The procedure is based on results on the lengths of upper triangular matrix algebras. Also the definition of the hereditary length of an algebra is introduced, and the problem of computing the hereditary lengths of matrix algebras is discussed.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06450-w