The expected number of Z-eigenvalues of a real gaussian tensor

Abstract

A real number $\lambda$ is called a Z-eigenvalue of a tensor $A$, if $\lambda$ is an eigenvalue of $A$ and the corresponding eigenvector $v$ is real and satisfies $v^{T}v=1$. In this paper we compute the expected number of Z-eigenvalues of a real gaussian tensor and its asymptotic behaviour. Here we call a tensor $A=(A_{i_0,\dots ,i_d})\in {\mathbb{R}}^{n^{d+1}}$ gaussian, when the $A_{i_0,\dots ,i_d}$ are centered gaussian random variables with variance ${\sigma }^2=1$.

11 pages, 1 figure

References in corpus (1)

• The Number of Eigenvalues of a Tensor