PIMS Special Seminar: Richard Brualdi (Wisconsin-Madison)

(0,1)-matrices are, in particular, nonnegative matrices, and so the Perron-Frobenius theory of nonnegative matrices applies to them. Thus they have a nonnegative eigenvalue that is at least as large as the magnitude of all other eigenvalues. Requiring all eigenvalues to be nonnegative imposes severe restrictions on a matrix. The class of matrices known as totally nonnegative (TNN) matrices is a proper subclass of the class of matrices with only nonnegative eigenvalues. TNN (0,1)-matrices have interesting properties and are characterized by four forbidden submatrices.

(This talk is based on joint research with Steve Kirkland.)