Department of Mathematics & Statistics
Discrete Math Seminar - Winter 2002
Monday, April 8, 1:30p.m., LB235
{Seminars}
Jordan Structures of Totally Nonnegative Matrices
Dr. Shaun Fallat
Abstract:
An n-by-n matrix is said to be totally nonnegative if every minor of A is nonnegative. The problem of interest is to characterize all possible Jordan canonical forms (Jordan structures) of irreducible totally nonnegative matrices. We demonstrate key relationships between the number and sizes of the Jordan blocks corresponding to zero and derive many relationships between all the possible ranks and principal ranks of irreducible totally nonnegative matrices. The main tools used are the acyclic weighted diagrams (or digraphs) associated with bidiagonal factorizations of totally nonnegative matrices.