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Mathematics Colloquium: Playing with matrices-will they always do what we want them to?
4:10 pm, Neill Hall 5W
Abstract: We start with a matrix (or array) where some entries are specified but unknown. The question is this: no matter what those entries are-as long as they fulfill some certain conditions-can we fill in the rest of the entries so that we have a matrix of a certain type? We will look at P0, 1-matrices and sign symmetric P0, 1-matrices. A P0, 1-matrix is a matrix where the diagonal entries are positive and every principal minor is nonnegative. A sign symmetric P0, 1-matrix is a P0, 1-matrix with the added condition that for any entry aij, either aij = aji = 0 or aijaji > 0. We use graphs and digraphs in order to classify the matrices. I will define most terms (including the ones not defined in the abstract) so come and see what this is all about!