Almost-commuting matrices are almost jointly diagonalizable

Abstract

We study the relation between approximate joint diagonalization of self-adjoint matrices and the norm of their commutator, and show that almost commuting self-adjoint matrices are almost jointly diagonalizable by a unitary matrix.

Minor corrections; results unchanged

References in corpus (2)

• Almost commuting matrices with respect to normalized Hilbert-Schmidt norm
• A Hilbert-Schmidt analog of Huaxin Lin's Theorem

Cited by in corpus (3)

• Making Laplacians commute
• Approximate symmetries of Hamiltonians
• Asymptotic metrics on the space of matrices under the commutation relation