Inequalities on Generalized Tensor Functions with Diagonalizable and Symmetric Positive Definite Tensors

Abstract

The main purpose of this paper is to investigate inequalities on symmetric sums of diagonalizable and positive definite tensors. In particular, we generalize the well-known Hlawka and Popoviciu inequalities to the case of diagonalizable and positive definite tensors. As corollaries, we extend Hlawka and Popoviciu inequalities for the combinatorial determinant, permanent and immanant of tensors, and generalized tensor functions.

Permanents of multidimensional matrices: Properties and applications

“…One can find many various multidimensional matrix operations and tensor products in the literature, for example, [2,5,10,15]. We do not aim to observe all of them here.…”