Department of Mathematics

Tensor rank over a noncommutative division ring behaves quite differently from the commutative theory: coefficients cannot be moved freely between factors, and even interchanging two modes can change the rank.

In this talk I consider third-order tensors over the quaternions with two middle slices, which can be studied through matrix pencils and their Kronecker canonical forms.

I will explain how complex adjoint representations can be used to understand quaternion rank in this setting, and discuss how quaternion rank compares with the rank of the same tensor viewed over the complex numbers.

The talk is based on recent work.