| New Results on Sign Patterns that Allow Diagonalizability |
| Received:March 04, 2021 Revised:July 14, 2021 |
| Key Words:
sign pattern allowing diagonalizability maximum cycle length minimum rank maximum rank Frobenius normal form
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| Fund Project:Supported by Research Project of Leshan Normal University (Grant No.LZD016). |
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| Abstract: |
| Characterization of sign patterns that allow diagonalizability has been a long-standing open problem. In this paper, we obtain some sufficient and/or necessary conditions for a sign pattern to allow diagonalizability. Moreover, we determine how many entries need to be changed to obtain a matrix $B'\in Q(A)$ with rank ${\rm MR}(A)$ from a matrix $B \in Q(A)$ with rank ${\rm mr}(A)$. Finally, we also obtain some results on a sign pattern matrix in Frobenius normal form that allows diagonalizability. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2022.02.001 |
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