Re: sylvester_matrix?

[Svante Signell]

On Sun, 2011-05-01 at 12:20 -0700, Rik wrote:
> 5/1/11
> 
> John,
> 
> I just reviewed the documentation on Famous Matrices and there is a
> function (sylvester_matrix) which produces a matrix form that I was unable
> to verify.  The form that Wikipedia documents
> (http://en.wikipedia.org/wiki/Sylvester_matrix) is more akin to toeplitz or
> hankel in that it starts with two input polynomials, rather than a single
> scalar input.  Do you have a better idea about what this function is
> actually creating?

Looks like this matrix is the same as the Hadamard matrix, i.e.
sylvester_matrix(k) = hadamard(2^k). These matrices are used to create
orthogonal vectors (rows and columns are orthogonal) in coding theory
for error detection and correction.

See 
http://en.wikipedia.org/wiki/Hadamard_code
and
http://en.wikipedia.org/wiki/Hadamard_matrix