On the Complete Pivoting Conjecture for a Hadamard Matrix of Order
نویسنده
چکیده
This paper settles a conjecture by Day and Peterson that if Gaussian elimination with complete pivoting is performed on a 12 by 12 Hadamard matrix, then must be the (absolute) pivots. In contrast, at least 30 patterns for the absolute values of the pivots have been observed for 16 by 16 Hadamard matrices. This problem is non-trivial because row and column permutations do not preserve pivots. A naive computer search would require (12!) 2 trials.
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