Lek-Heng Lim : Hypermatrices

Posted by Mihnea Popa , part of the Departmental Colloquium.

At

April 26, 2013, 3 p.m.

In

SEO 636

Abstract

This talk is intended for those who, like the speaker, have at some point wondered whether there is a theory of three- or higher- dimensional matrices that parallels matrix theory. We will discuss how notions like rank, norm, determinant, eigen and singular values may be generalized to hypermatrices. We will see that, far from being artificial constructs, these notions have appeared naturally in a wide range of applications: chemistry (fluorescence spectroscopy, density matrix renormalization group), computer science (matrix multiplication complexity, quantum computing), optimization (self-concordance, higher-order optimality conditions), statistics (higher-order moments and cumulants, minimum rank matrix completion), physics (quark states, Yang-Baxter equations), and signal processing (antenna array processing, CDMA radio communication).