Professor Can Chen

School of Data Science and Society (SDSS) and Department of Mathematics

The University of North Carolina at Chapel Hill

Title: The Kronecker product of tensors

Abstract:

Tensors extend classic matrix theory to account for multiway relationships, which are ubiquitous in engineering, biological, and social systems. While the Kronecker product is a potent tool for analyzing the coupling of systems in the matrix context, its utility in studying multiway interactions with tensors remains relatively unexplored. In this talk, I will present a comprehensive investigation of algebraic, structural, and spectral properties of the tensor Kronecker product. Additionally, I will express various tensor decompositions and tensor eigenvalues in terms of the tensor Kronecker product. Finally, I will provide numerical examples to demonstrate the advantages of the tensor Kronecker product in computing tensor decompositions and Z-eigenvalues.

The talks will be both in-person at Chapman Hall 435 and on Zoom: https://unc.zoom.us/j/96417451559.