Almost-commuting matrices are almost jointly diagonalizable

2013/05/07 by Klaus Glashoff, Glashoff, Klaus, Michael M. Bronstein +1
Computer Science · Mathematics · #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Random Matrices and Applications #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1305.2135

openalex publication_date 2013/05/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• The Frobenius norm and the commutator

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• Vector-wise Joint Diagonalization of Almost Commuting Matrices
• Almost commuting matrices with respect to the rank metric
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• Approximate diagonalization of self--adjoint matrices over C(M)