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Generating Systems of the Full Matrix Algebra That Contain Nonderogatory Matricesстатья
Статья опубликована в журнале из списка Web of Science и/или Scopus
- Журнал: Journal of Mathematical Sciences
- Том: 262
- Номер: 1
- Год издания: 2022
- Издательство: Plenum Publishers
- Местоположение издательства: United States
- Первая страница: 99
- Последняя страница: 107
- DOI: 10.1007/s10958-022-05802-2
- Аннотация: Let 𝒜 be an algebra over a field 𝔽 generated by a set of matrices 𝒮. The paper considers algorithmic aspects of checking whether 𝒜 coincides with the full matrix algebra. Laffey has shown that for 𝔽 = ℂ, under the assumption that 𝒮 contains a Jordan matrix from a certain class, there is a fast method for checking whether 𝒜 possesses nontrivial invariant subspaces and, consequently, coincides with the full algebra by Burnside’s theorem. This paper extends the class to the largest subclass of Jordan matrices on which the algorithm works correctly. Examples demonstrating different types of behavior of other matrix systems are provided.