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It would be helpful to give examples. One interesting pair of matrices with this property would be the matrices used by Heisenberg to describe the harmonic oscillator in matrix mechanics, for which XP − PX = the identity matrix (multiplied by iħ), which clearly commutes with both X and P. It would also be helpful to show a pair of functions with this property. Dirac66 (talk) 00:03, 1 May 2014 (UTC)[reply]