20 Aug
2012
20 Aug
'12
5:41 p.m.
On Mon, Aug 20, 2012 at 9:58 AM, Warren Smith <warren.wds@gmail.com> wrote:
OK, my searcher has now found matrices of the form Toeplitz*Hankel, where * denotes Hadamard elementwise matrix product (C=A*B means C_ij=A_ij B_ij) where both A and B are sign matrices, which achieve the maximum possible |determinant| among ALL matrices of size N with entries in [-1,1], for EVERY N=1,2,3,...,13 (and N=16). See http://oeis.org/A003433 .
It follows from your computation that some Hadamard matrices of order can be factored in this way. Question: Do all Hadamard matrices<http://en.wikipedia.org/wiki/Hadamard_matrix>have such a factorization? I would guess not.