Abstract
I will focus on one special case of tensor decomposition — symmetric tensors and Waring decomposition. I will start by discussing the naive approach, then I will discuss Sylvester's algorithm for binary forms. As a bonus I will show how Sylvester's algorithm for symmetric tensor decomposition also gives a method find the roots of a cubic polynomial in one variable.
I will discuss what to expect regarding generic rank and uniqueness of tensor decomposition. With the remaining time I will discuss the recently defined notion of an eigenvector of a (symmetric) tensor (Lim05, Qi05), which leads to a new method (developed with Ottaviani) for exact Waring decomposition.
The first session of this talk will take place on Wednesday, September 3 from 9:00 am – 10:00 am.