New results on sign patterns that allow diagonalizability
Received:March 04, 2021  Revised:July 14, 2021
Key Word: Sign pattern   Allow diagonalizability   Maximum cycle length   Frobenius normal form sign pattern matrix  
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Xinlei Feng Leshan Normal University No.778, Binhe road, Leshan
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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 B0 ∈ Q(A) with rank MR(A) from a matrix B ∈ Q(A) with rank mr(A). Finally, we also obtain some results on a sign pattern matrix in Frobenius normal form that allows diagonalizability.
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