Von Neumann's inequality for tensors

Abstract

For two matrices in ${\mathbb{R}}^{n_1\times n_2}$, the von Neumann inequality says that their scalar product is less than or equal to the scalar product of their singular spectrum. In this short note, we extend this result to real tensors and provide a complete study of the equality case.

References in corpus (1)

• A New Convex Relaxation for Tensor Completion

Cited by in corpus (2)

• Convex recovery of tensors using nuclear norm penalization
• On the subdifferential of symmetric convex functions of the spectrum for symmetric and orthogonally decomposable tensors