New Results on Sign Patterns that Allow Diagonalizability
Received:March 04, 2021  Revised:July 14, 2021
Key Word: sign pattern   allowing diagonalizability   maximum cycle length   minimum rank   maximum rank   Frobenius normal form
Fund ProjectL:Supported by Research Project of Leshan Normal University (Grant No.LZD016).
 Author Name Affiliation Xinlei FENG College of Mathematics and Physics, Leshan Normal University, Sichuan 614000, P. R. China Zhongshan LI Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30302, USA
Hits: 179
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.