A matrix is called totally nonnegative if each of its square submatrices has a nonnegative determinant. Such matrices arise in a variety of applications such as differential equations, chemistry, and stochastic processes. The Vandermonde matrix and the Hilbert matrix are examples of totally nonnegative matrices.

We will discuss combinatorial interpretations of such matrices and of related functions called totally nonnegative polynomials. Some familiarity with linear algebra will be helpful but not necessary.

USG funded