Multiplicities of Eigenvalues of Tensors

In linear algebra, there are two versions of multiplicities of eigenvalues. One is the multiplicity (algebraic multiplicity) of an eigenvalue in the characteristic polynomial and the other is the dimension (geometric multiplicity) of the eigenspace corresponding to this eigenvalue. It is well known that the algebraic multiplicity is no smaller than the geometric multiplicity. Eigenvalues of tensors are generalizations of eigenvalues of matrices. One can define algebraic and geometric multiplicities of an eigenvalue of a tensor. In this talk, I will discuss relations between algebraic multiplicities and geometric multiplicities of an eigenvalue of a tensor. This is a joint work with Shenglong Hu.