Algebra/Linear Algebra Seminar

Speaker: Wei Gao

Title: Sign Patterns and Point-Hyperplane Configurations

Abstract: A sign pattern (matrix) is a matrix whose entries are from the set \(\{+, -, 0\}\). The minimum rank of a sign pattern matrix is the minimum of the ranks of the real matrices whose entries have signs equal to the corresponding entries of the sign pattern. In this talk, we establish a direct connection between condensed sign patterns with minimum rank r and point-hyperplanes configurations in \(R^{r-1}\), and we use this connection to prove some interesting results.