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Mathematical background

Let $H$ be the set of vector with components either -1 or 1 and the scalar matrices ${\bf A^{uv}}$, ${\bf u},{\bf v}\in H$,the set of matrices whose elements are

A^{{\bf u}{\bf v}}_{ij}=
...= -1,
\underline{a_{ij}}~{\rm if}~u_i.v_j= 1

The set of matrices ${\bf A^{uv}}$ has $2^{2n-1}$ elements. If all matrices in the set have a determinant of the same sign, then all the matrices A are regular [22].

Note than another simplification procedure may be built by using the spectral radius (see section 7.6).

Jean-Pierre Merlet 2012-12-20