Linear Algebra Seminar

Special day: April 23, 2014       Special place: Parker 320     SAME TIME

Speaker: Ben Reames

Title:  Singular Vector Tuples for Tensors

Abstract: The Singular Value Decomposition is a simple but powerful generalization to arbitrary matrices of the unitary diagonalization of normal matrices. One of the many applications of the SVD is the computation of best rank r approximations to a given matrix M. A natural question is whether an analog to this technique exists for higher-order tensors. In this talk, I will introduce the notion of a singular vector tuple of a tensor as the proper extension of the singular vectors of a matrix, following the recent paper "The number of singular vector tuples and uniqueness of best rank one approximation of tensors" by Friedland and Ottaviani. I will discuss some of the results of the paper and show the relation of singular vector tuples to the problem of finding a best rank one approximation to a tensor.