Positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums

TL;DR

This paper establishes necessary and sufficient conditions for transforming a nonnegative tensor into one with specified slice sums through positive diagonal scaling, extending classical matrix scaling results to tensors.

Contribution

It introduces new conditions, based on Bapat-Raghavan and Franklin-Lorenz criteria, for diagonal scaling of nonnegative tensors to achieve prescribed slice sums.

Findings

Derived necessary and sufficient conditions for tensor scaling.

Extended classical matrix scaling results to higher-order tensors.

Provided theoretical framework for tensor normalization with prescribed sums.

Abstract

In this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums. These conditions are variations of Bapat-Raghavan and Franklin-Lorenz conditions.