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nLab > Latest Changes: diagonal matrix

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  1.  
    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeMay 21st 2024

    I have corrected the statement about the diagonal matrices forming the center: an additional condition is necessary, for example that the ring is an algebraically closed field (Schur lemma).

    diff, v8, current

  2. This is patently false. ((1,0),(0,−1)) and ((1,2),(2,1)) don’t commute. Diagonal matrices commute with other diagonal matrices but not with general square matrices.

    ken

    diff, v9, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeFeb 12th 2025

    Oh dear.

    Let’s say: The diagonal matrices form a non-central commutative subalgebra of the matrix algebra Matn×n(R), isomorphic to the nfold direct sum of the ground ring.

    diff, v10, current

1 to 3 of 3

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