Publicação
The jordan form problem for C=AB : the balanced, diagonalizable case
| Resumo: | We consider a key case in the fundamental and substantial prob- lem of the possible Jordan canonical forms of A;B;C \in Mn(F) when C = AB. If A \in M2k(F) (respectively B;C \in M2k(F) ) is diagonalizable with two distinct eigenvalues a1; a2 (respectively b1; b2, and c1; c2), each with multiplicity k, and when C = AB, all possibilities for a1; a2; b1; b2; c1; c2 are characterized. The possibilities are much more restrictive than the ob- vious determinant condition: (a1a2b1b2)k = (c1c2)k allows. This is then used to settle the general, two eigenvalue per matrix, diagonalizable case of the Jordan form problem for C = AB. |
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| Autores principais: | Johnson, Charles R. |
| Outros Autores: | Zhang Yulin |
| Assunto: | Jordan form Matrix product Rank Null space null space, rank |
| Ano: | 2010 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | We consider a key case in the fundamental and substantial prob- lem of the possible Jordan canonical forms of A;B;C \in Mn(F) when C = AB. If A \in M2k(F) (respectively B;C \in M2k(F) ) is diagonalizable with two distinct eigenvalues a1; a2 (respectively b1; b2, and c1; c2), each with multiplicity k, and when C = AB, all possibilities for a1; a2; b1; b2; c1; c2 are characterized. The possibilities are much more restrictive than the ob- vious determinant condition: (a1a2b1b2)k = (c1c2)k allows. This is then used to settle the general, two eigenvalue per matrix, diagonalizable case of the Jordan form problem for C = AB. |
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