On a multi-dimesional generalization of the notion of orthostochastic and unistochastic matrices

TL;DR

This paper introduces a multi-dimensional generalization of orthostochastic, unistochastic, and qustochastic matrices, expanding their mathematical framework motivated by physics, and explores their fundamental properties.

Contribution

It defines and analyzes $d$-orthostochastic, $d$-unistochastic, and $d$-qustochastic matrices, extending classical concepts to higher dimensions and different number fields.

Findings

Introduces $d$-orthostochastic, $d$-unistochastic, and $d$-qustochastic matrices.

Establishes basic properties of these generalized matrices.

Connects the concepts to mathematical physics.

Abstract

We introduce the notions of $d$-orthostochastic, $d$-unistochastic, and $d$-qustochastic matrices. These are the particular cases of $F^d$-bistochastic matrices where $F$ is real or complex numbers or quaternions. The concept is motivated by mathematical physics. When $d=1$, we recover the orthostochastic, unistochastic, and qustochastic matrices respectively. This work exposes the basic properties of $F^d$-bistochastic matrices.