Asymptotic metrics on the space of matrices under the commutation relation

Abstract

We show that the norm of the commutator defines "almost a metric" on the quotient space of commuting matrices, in the sense that it is a semi-metric satisfying the triangle inequality asymptotically for large matrices drawn from a "good" distribution.

Minor correction; results unchanged

References in corpus (1)

• Almost-commuting matrices are almost jointly diagonalizable