New Results on Sign Patterns that Allow Diagonalizability

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'∈ 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.