Two 12 by 12 hadamard matrices. Are they the same? Rules of transformation: by a diagonal matrix with 1, -1's down the diagonal (change sign at an index); by a permuation matrix (swaping rows or columns, that is, a relabling). Francois 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 -1 1 -1 -1 -1 1 1 1 -1 1 1 1 1 -1 1 -1 -1 -1 1 1 1 -1 1 -1 1 1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 1 -1 1 -1 -1 -1 1 1 1 1 1 -1 1 1 -1 1 -1 -1 -1 1 -1 1 1 1 -1 1 1 -1 1 -1 -1 1 -1 -1 1 1 1 -1 1 1 -1 1 -1 1 -1 -1 -1 1 1 1 -1 1 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 1 1 -1 1 -1 1 -1 -1 -1 1 1 1 -1 1 1 Burt 1 1 1 1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 1 1 1 1 -1 1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 1 1 -1 -1 1 1 1 1 -1 1 1 -1 1 1 1 1 -1 1 -1 1 -1 1 1 1 -1 1 -1 1 1 -1 1 -1 1 1 1 1 -1 1 1 -1 1 1 -1 -1 1 1 1 1 1 -1 -1 1 -1 1 1 1 1 -1 1 1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 -1 1 1 1 -1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 1 After swapping signs per col so that the number of 1's and -1's are the same for both solutions: Francois 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 -1 1 1 1 -1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 1 -1 -1 -1 1 -1 -1 1 1 1 -1 1 1 1 -1 -1 -1 1 -1 -1 Burt 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 1 1 1 -1 -1 1 1 -1 -1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 1 -1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 1 -1 1 1 -1 -1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 -1 1 -1 1 1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 -1 -1 1 1 1 1 -1 -1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 1 1 -1 1 -1 1 -1 After row multiplcation of Burt to get first col. correct: Francois 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 1 -1 1 1 1 -1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 1 -1 -1 -1 1 -1 -1 1 1 1 -1 1 1 1 -1 -1 -1 1 -1 -1 Burt 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 1 1 1 -1 -1 1 1 -1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 1 -1 1 1 1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 -1 -1 1 1 1 1 -1 1 -1 1 -1 1 1 -1 -1 -1 -1 1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 Swapping rows and col to get second row the same: Francois 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 1 1 -1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 1 1 -1 -1 -1 1 1 1 -1 -1 1 1 -1 Burt 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 1 -1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 1 -1 -1 -1 1 -1 1 1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 Swapping rows to get a pattern in the first 6 cols Francois 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 -1 1 -1 1 1 -1 1 -1 1 1 -1 -1 1 -1 1 -1 1 -1 1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 -1 1 -1 1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 1 -1 1 -1 -1 1 -1 1 1 1 -1 -1 1 -1 -1 1 1 -1 -1 -1 1 1 -1 1 1 -1 -1 1 -1 1 1 1 -1 -1 -1 1 1 -1 -1 -1 1 1 1 -1 -1 1 1 -1 Burt 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 1 -1 1 1 -1 -1 1 1 -1 1 -1 -1 -1 1 1 -1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1 1 1 -1 -1 1 -1 -1 1 -1 1 -1 1 1 1 -1 -1 -1 1 1 1 -1 -1 1 1 1 -1 1 -1 1 -1 -1 -1 1 -1 1 1 1 -1 1 -1 -1 1 -1 1 -1 1 1 -1 1 -1 -1 1 1 -1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 1 1 -1 1 1 -1 -1 -1 1 1 1 1 1 -1 -1 -1 Now Burt's 7-th col. alternates, and there are no alternating col's in Francois. What are we to make of this?