Colloquium: "Barrett-Johnson inequalities for totally nonnegative matrices"

Speaker: Mark Skandera, Lehigh University

Abstract: The classes of positive semidefinite matrices and totally nonnegative matrices may be characterized in terms of the nonnegativity of certain minors.  These nonnegativity conditions in turn imply that products of the minors satisfy other inequalities. Some such inequalities, first stated by Hadamard, Fischer, and Koteljanskii, apply both to positive semidefinite matrices and to totally nonnegative matrices. More recently, Barrett and Johnson considered averages of certain products of minors, and showed that in positive semidefinite matrices, such averages satisfy simple inequalities. We show that the Barrett-Johnson inequalities hold for totally nonnegative matrices as well. This is joint work with Daniel Soskin.

Hosts: Martha Precup and John Shareshian

Tea will be served at 3:30pm in room 200.

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