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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.
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Almost eigenvectors for almost commuting matrices
A. Bernstein · 1971
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Almost commuting matrices
Carl Pearcy and Allen Shields · 1979
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J. F. Cardoso · 1994
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