Further results on discrete unitary invariance

TL;DR

This paper generalizes previous results on discrete unitary invariance, extending the class of functions of matrices that decompose under symmetry sums, and addresses an open problem from earlier work.

Contribution

It broadens the scope of discrete unitary invariance results and resolves a previously posed open problem.

Findings

Extended invariance results to a larger class of matrix functions

Provided a solution to an open problem in the original Marcus paper

Enhanced understanding of symmetry-based matrix function decompositions

Abstract

In arXiv:1607.06679, Marcus proved that certain functions of multiple matrices, when summed over the symmetries of the cube, decompose into functions of the original matrices. In this note, we generalize the results from the Marcus paper to a larger class of functions of multiple matrices. We also answer a problem posed in the Marcus paper.