Pure Maths Colloquium: Elina Robeva

Tensor decomposition has many applications. However, it is often a hard problem. In this talk we discuss a family of tensors, called orthogonally decomposable tensors, which retain many of the nice properties of matrices that general tensors don’t. A symmetric tensor is orthogonally decomposable if it can be written as a linear combination of tensor powers of \(n\) orthonormal vectors. We will see that the decomposition of such tensors can be found efficiently, their eigenvectors can be computed efficiently, and the set of orthogonally decomposable tensors of low rank is closed and can be described by a set of quadratic equations. Analogously, we study nonsymmetric orthogonally decomposable tensors, and show that the same results hold. Finally, we discuss a generalization called orthogonal tensor networks, which allows to find an efficient decomposition of a larger set of tensors.