A theory of functions of several variables applied to square matrices

TL;DR

This paper proposes a new definition for functions of multiple variables applied to square matrices, aligning with traditional matrix functions, and provides computational rules, differentiation formulas, and potential applications.

Contribution

It introduces a consistent multi-variable matrix function definition and derives fundamental computational and differentiation rules, expanding the theoretical framework.

Findings

Provides a formal definition for multivariable functions of matrices

Derives basic computational rules for these functions

Includes examples demonstrating potential applications

Abstract

In this paper, we give one possible definition for functions of several variables applied to endomorphisms of finite dimensional C-vector spaces. This definition is consistent with the usual notion of a function of a square matrix. Some basic rules of computation are given, as well as a formula for differentiation of it. A few examples of possible applications is also given at the end of the article.