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


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