= Centralizer of a diagonal matrix
{title2=$C(D)=\{B:BD=DB\}$}
For a <diagonal matrix> $D=\operatorname{diag}(d_1,\ldots,d_n)$ over a <field>, <matrix multiplication> gives $(BD-DB)_{ij}=(d_j-d_i)b_{ij}$. Hence a <matrix> $B$ <commutes> with $D$ exactly when $b_{ij}=0$ wherever $d_i\ne d_j$. If all diagonal entries are distinct, the <centralizer of a diagonal matrix> consists exactly of <diagonal matrices>. When entries repeat, the allowed entries form unrestricted blocks on the corresponding <eigenspaces>.
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