Totally Nonnegative (0,1) Matrices

Speaker: Prof Steve Kirkland (Hamilton Institute, NUIM)

Time: 4:00PM

Date: Mon 12th October 2009

Location: Mathematical Sciences Seminar Room

Motivated by a result of McKay et al, we investigate the class of square (0,1) matrices which have all of their eigenvalues equal to nonnegative real numbers. We pay particular attention to the (0,1) totally nonnegative matrices -- i.e. those (0,1) matrices with the property that every square submatrix has nonnegative determinant. Over the class of irreducible (0,1) totally nonnegative matrices of order n, we determine those matrices having minimum spectral radius, and discuss the maximum number of zeros for such matrices. Joint work with Richard Brualdi.

(This talk is part of the Algebra/Claude Shannon Institute series.)