The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group


with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

Non-commutative arithmetic-geometric mean inequalities.

Ben Recht, Professor, Dept. of Computer Science and Dept. of Electrical Engineering

Date and Time: Sep 22, 2010 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building


The arithmetic-geometric mean inequality states that the arithmetic mean of a set of positive numbers is always greater than the geometric mean unless all of the numbers are equal to one another. Does a similar inequality hold for positive definite matrices? The answer is not straightforward as positive definite matrices do not commute and there are myriad possible connotations of "greater than." I will discuss how we might use a "non-commutative" arithmetic geometric mean inequality in control, signal processing, and optimization applications, but will also show that such an inequality does not generally hold. Instead, I will describe a weaker inequality that is true, and explore some conjectures about how this bound might be strengthened.