Simultaneous unitary equivalences

Abstract

Let A, B, C, D be given finite sets of pairs of n-by-n complex matrices. We describe an algorithm to determine, with finitely many computations, whether there is a single unitary matrix U such that each pair of matrices in A is unitarily similar via U, each pair of matrices in B is unitarily congruent via U, each pair of matrices in C is unitarily similar via \bar{U}, and each pair of matrices in D is unitarily congruent via \bar{U}.

10 pages

References in corpus (1)

• Unitary and Euclidean representations of a quiver

Cited by in corpus (7)

• Unitary and orthogonal equivalence of sets of matrices
• Specht's criterion for systems of linear mappings
• Local unitary equivalence of quantum states and simultaneous orthogonal equivalence
• Remarks on the classification of a pair of commuting semilinear operators
• The quantum separability problem is a simultaneous hollowisation matrix analysis problem
• Simultaneous Stoquasticity
• Mutually-orthogonal unitary and orthogonal matrices