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Asymptotic metrics on the space of matrices under the commutation relation
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matricesspacealmostasymptoticasymptoticallycommutationcommutatorcommuting
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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.
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