3 papers
math.MG2025
Testing isomorphism between tuples of subspaces
Emily J. King, Dustin G. Mixon, Shayne Waldron
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 wh…
math.FA2025
Tight frames over the quaternions and equiangular lines
Shayne Waldron
We show that much of the theory of finite tight frames can be generalised to vector spaces over the quaternions. This includes the variational characterisation, group frames, and t…
cs.IT2024
Equations for the overlaps of a SIC
Len Bos, Shayne Waldron
We give a holomorphic quartic polynomial in the overlap variables whose zeros on the torus are precisely the Weyl-Heisenberg SICs (symmetric informationally complete positive opera…