On the largest multilinear singular values of higher-order tensors

Ignat Domanov, Alwin Stegeman, Lieven De Lathauwer

Let ${\sigma }_n$ denote the largest mode-$n$ multilinear singular value of an $I_1\times \cdots \times I_N$ tensor $\mathcal{T}$. We prove that $$ σ_1^2+\dots+σ_{n-1}^2+σ_{n+1}^2+\dots+σ_{N}…