On the number of invariant factors of matrix products
We prove an inequality relating the number of nontrivial invariant factors of n × n matrices A and B, with those of AB, and get some results on the cases of equality. In particular, we characterize the similarity classes, and , with all eigenvalues in the base field, such that AB is nilpotent for so...
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| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2005
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| Assuntos: | |
| Texto completo: | http://hdl.handle.net/10316/4631 |
| País: | Portugal |
| Oai: | oai:estudogeral.sib.uc.pt:10316/4631 |
| Resumo: | We prove an inequality relating the number of nontrivial invariant factors of n × n matrices A and B, with those of AB, and get some results on the cases of equality. In particular, we characterize the similarity classes, and , with all eigenvalues in the base field, such that AB is nilpotent for some and . |
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