Commutativity of Matrices Up to a Matrix Factor
| Autor: | O. V. Markova, N. A. Kolegov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Pure mathematics Applied Mathematics General Mathematics 010102 general mathematics Diagonalizable matrix Space (mathematics) 01 natural sciences 010305 fluids & plasmas law.invention Matrix (mathematics) Invertible matrix law 0103 physical sciences Canonical form 0101 mathematics Connection (algebraic framework) Commutative property Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Journal of Mathematical Sciences. 249:209-220 |
| ISSN: | 1573-8795 1072-3374 |
| Popis: | The matrix relation AB = CBA is investigated. An explicit description of the space of matrices B satisfying this relation is obtained for an arbitrary fixed matrix C and a diagonalizable matrix A. The connection between this space and the family of right annihilators of the matrices A−λC, where λ ranges over the set of eigenvalues of the matrix A, is studied. In the case where AB = CBA, AC = CA, and BC = CB, a canonical form for A,B,C, generalizing Thompson’s result for invertible A,B,C, is introduced. Also bounds for the lengths of pairs of matrices {A,B} of the form indicated are provided. Bibliography: 26 titles. |
| Databáze: | OpenAIRE |
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