Matrix identities involving multiplication and transposition

TL;DR

This paper investigates algebraic identities involving matrix multiplication and unary operations like transposition and Moore-Penrose inversion, demonstrating that many such identities cannot be finitely characterized.

Contribution

It provides new results showing the non-existence of finite bases for certain matrix identities involving these operations.

Findings

Many matrix identities with transposition and Moore-Penrose inversion have no finite basis.

The study advances understanding of algebraic structures in matrix theory.

Results impact the algebraic characterization of matrix operations.

Abstract

We study matrix identities involving multiplication and unary operations such as transposition or Moore-Penrose inversion. We prove that in many cases such identities admit no finite basis.