Algorithms for orbit closure separation for invariants and semi-invariants of matrices

Abstract

We consider two group actions on $m$-tuples of $n\times n$ matrices. The first is simultaneous conjugation by ${\mathrm{GL}}_n$ and the second is the left-right action of ${\mathrm{SL}}_n\times {\mathrm{SL}}_n$. We give efficient algorithms to decide if the orbit closures of two points intersect. We also improve the known bounds for the degree of separating invariants in these cases.

Better bounds for separating invariants and improved exposition in some sections

References in corpus (2)

• An improved bound for the length of matrix algebras
• Polynomial bound for the nilpotency index of finitely generated nil algebras

Cited by in corpus (8)

• Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopes
• The minimal canonical form of a tensor network
• Separating invariants over finite fields
• Degree bounds for fields of rational invariants of $\mathbb{Z}/p\mathbb{Z}$ and other finite groups
• Ranks of linear matrix pencils separate simultaneous similarity orbits
• Separating G_2-invariants of several octonions
• Classification of G_2-orbits for pairs of octonions
• On m-tuples of nilpotent 2x2 matrices over an arbitrary field