**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).

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