Orthogonal Tensor Decomposition

Applied Math And Analysis Seminar

Elina Robeva (MIT)

Friday, November 30, 2018 -
3:15pm to 4:15pm
Physics 119

A symmetric tensor is orthogonally decomposable if it can be written as a linear combination of tensor powers of n orthonormal vectors. Such tensors are interesting because their decomposition can be found efficiently. We study their spectral properties and give a formula for all of their eigenvectors. We also give equations defining all real symmetric orthogonally decomposable tensors. Analogously, we study nonsymmetric orthogonally decomposable tensors, describing their singular vector tuples and giving polynomial equations that define them. In an attempt to extend the definition to a larger set of tensors, we define tight-frame decomposable tensors and show that for certain equiangular tight frames they too can be decomposed via the tensor power method.

Last updated: 2018/12/16 - 10:21pm