For any n at least 2 and ranks j,k up to floor(n/2), a normal matrix on C^n has off-diagonal corner ranks (k,j); in infinite dimensions all pairs 0 <= j,k <= infinity occur.
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Normal operators with highly incompatible off-diagonal corners
For any n at least 2 and ranks j,k up to floor(n/2), a normal matrix on C^n has off-diagonal corner ranks (k,j); in infinite dimensions all pairs 0 <= j,k <= infinity occur.