Testing isomorphism between tuples of subspaces
Emily J. King, Dustin G. Mixon and Shayne Waldron
Abstract:
Given two tuples of subspaces, can you tell whether the tuples are isomorphic?
We develop theory and algorithms to address this fundamental question. We focus on
isomorphisms in which the ambient vector space is acted on by either a unitary group
or general linear group. If isomorphism also allows permutations of the subspaces,
then the problem is at least as hard as graph isomorphism. Otherwise, we provide
a variety of polynomial-time algorithms with Matlab implementations to test for
isomorphism.
Keywords:
subspace isomorphism, Grassmannian, Bargmann invariants,
H*-algebras, quivers, graph isomorphism
Math Review Classification:
Primary 4M15, 05C60, 81R05, 16G20;
Secondary
Length: 23 Pages
Last Updated: 21 May 2024
Availability: