Why the 'Sharpest' Rotations Are Just Permutations
If you take a table of numbers where the sum of squares in each row and column is 1, and you want to maximize the sum of fourth powers, the answer will only be permutations of coordinates. The fourth power sharply penalizes division: 0.5 gives only 0.0625, while 1 remains 1. It's advantageous to give the entire weight of a row and column to one cell, filling it with +1 or -1, and the rest with zeros.