Physical Sciences and Mathematics Commons^™

Totally Nonnegative Matrices, Shaun M. Fallat

Dissertations, Theses, and Masters Projects

An m-by-n matrix A is called totally nonnegative (resp. totally positive) if the determinant of every square submatrix (i.e., minor) of A is nonnegative (resp. positive). The class of totally nonnegative matrices has been studied considerably, and this class arises in a variety of applications such as differential equations, statistics, mathematical biology, approximation theory, integral equations and combinatorics. The main purpose of this thesis is to investigate several aspects of totally nonnegative matrices such as spectral problems, determinantal inequalities, factorizations and entry-wise products. It is well-known that the eigenvalues of a totally nonnegative matrix are nonnegative. However, there are many …