UBC Mathematics Department
http://www.math.ubc.ca

## Colloquium Abstract: Professor Lon Rosen, Department of Mathematics, UBC

### Which functions preserve nonnegative symmetric matrices?

If A is a nonnegative, symmetric n\times n matrix, which functions of A yield a nonnegative matrix? We answer this question by exploiting a self-avoiding random walk representation for powers of a matrix. The answer provides a solution to the positive minorant problem: if 0\leq A\leq B in the sense that 0\leq a_{ij}\leq b_{ij}, do their \cal C_p norms satisfy ||A||_p \leq ||B||_p?

The prerequisite for this non-technical talk is that you have passed Math 221 (or, at least, taught it).