Seminar No.1550 Sign patterns that allow diagonalizability

Created Date 12/4/2017 福平   View Numbers  492 Return    

Title:  Sign patterns that allow diagonalizability
Reporter:  Prof. Zhongshan Li (Georgia State University)
Time: 2017-12-11 (Monday) 14:00
Place: G507

Abstract:  A sign pattern (matrix) is a matrix whose entries are from the set $\{+,-, 0 \}$. A square sign pattern $\cal A$ is said to allow diagonalizability if there is a diagonalizable real matrix whose entries have signs specified by the corresponding entries of $\cal A$. Characterization of sign patterns that allow diagonalizability has been a long-standing open problem.
It is known that a sign pattern allows diagonalizability if and only if it allows rank principality. In this talk, we establish some new necessary/sufficient conditions for a sign pattern to allow diagonalizability, and explore possible ranks of diagonalizable matrices with a specified sign pattern. In particular, it is shown that every irreducible sign pattern with minimum rank 2 allows diagonalizability at rank 2 and also at the maximum rank.

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