# 三亚娱乐官方网站gm777.top是一家集三亚娱乐官方网站，三亚娱乐官方网站，三亚娱乐官方网站于一体的综合性娱乐公司，为玩家提供全方位的游戏体验，诚邀您的体验。

## 數學科學學院學術報告：Sign patterns that allow diagonalization

A sign pattern (matrix) is a matrix whose entries are from the set $\{+, -, 0 \}$. A square sign pattern $\cal A$ is said to allow diagonalization 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 diagonalization has been a long-standing open problem. It is known that a sign pattern allows diagonalization if and only if it allows rank-principality. In this talk, we establish some new necessary/sufficient conditions for a sign pattern to allow diagonalization, 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 diagonalization at rank 2 and also at the maximum rank. Sign patterns whose maximal zero submatrices are strongly disjoint are shown to allow diagonalization with the maximum rank.