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Algebra Seminar: Computing All Principal Minors of a Matrix and the Related Inverse Problem
1:10p.m. Neill 106W
Abstract: In this presentation we describe two algorithms. The first efficiently and robustly computes all the principal minors of any square complex matrix. In the second part of the talk we present conditions under which this process may be inverted and a matrix having a given set of principal minors may be computed from its principal minors. A result by R. Loewy characterizing when two matrices have the same principal minors is also discussed.