Matrix commutators: Their asymptotic metric properties and relation to approximate joint diagonalization

Klaus Glashoff, Michael M. Bronstein*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We analyze the properties of the norm of the commutator of two Hermitian matrices, showing that asymptotically it behaves like a metric, and establish its relation to joint approximate diagonalization of matrices, showing that almost-commuting matrices are almost jointly diagonalizable, and vice versa. We show an application of our results in the field of 3D shape analysis.

Original languageEnglish
Pages (from-to)2503-2513
Number of pages11
JournalLinear Algebra and Its Applications
Volume439
Issue number8
DOIs
StatePublished - 15 Oct 2013
Externally publishedYes

Funding

FundersFunder number
Seventh Framework Programme307047
European Research Council

    Keywords

    • Commutator
    • Joint diagonalizability
    • Pseudo-metric

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