The Spectral Theory of Tensors

Abstract:

In 2005, independently, Lim and I defined eigenvalues and eigenvectors of a real tensor, and explored their practical application in determining positive definiteness of an even degree multivariate form. This work extended the classical concept of eigenvalues of square matrices, forms an important part of numerical multi-linear algebra, and has found applications or links with automatic control, statistical data analysis, optimization, magnetic resonance imaging, solid mechanics, quantum physics, higher order Markov chains, spectral hypergraph theory, Finsler geometry, etc., and attracted attention of mathematicians from different disciplines. During May 30 - June 2 this year, The International Conference on The Spectral Theory of Tensors was held at the Chern Mathematics Research Institute at Nankai University, Tianjin. 42 researchers from different countries reported their results. In this talk, we will review the development of the spectral theory of tensors.