On minimal generating systems for matrix O(3)-invariants

TL;DR

This paper investigates the algebra of invariants for multiple 3x3 matrices under orthogonal transformations, identifying the maximal degree of generators needed with a deviation of 3.

Contribution

It provides a description of the maximal degree of elements in minimal generating systems for matrix O(3)-invariants, advancing understanding of their algebraic structure.

Findings

Maximal degree of generators described with deviation 3

Results applicable over fields with characteristic not equal to two

Enhances knowledge of invariant algebra structure for 3x3 matrices

Abstract

The algebra of invariants of several 3 x 3 matrices under the action of the orthogonal group by simultaneous conjugation is considered over a field of characteristic different from two. The maximal degree of elements of minimal system of generators is described with deviation 3.