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hadamard

PURPOSE ^

% Construct a Hadamard matrix @var{Hn} of size @var{n}-by-@var{n}. The

SYNOPSIS ^

function h = hadamard (n)

DESCRIPTION ^

% -*- texinfo -*-
% @deftypefn {Function File} {} hadamard (@var{n})
% Construct a Hadamard matrix @var{Hn} of size @var{n}-by-@var{n}.  The 
% size @var{n} must be of the form @code{2 ^ @var{k} * @var{p}} in which
% @var{p} is one of 1, 12, 20 or 28.  The returned matrix is normalized,
% meaning @code{Hn(:,1) == 1} and @code{H(1,:) == 1}.
%
% Some of the properties of Hadamard matrices are:
%
% @itemize @bullet
% @item
% @code{kron (@var{Hm}, @var{Hn})} is a Hadamard matrix of size 
% @var{m}-by-@var{n}.
% @item
% @code{Hn * Hn' == @var{n} * eye (@var{n})}.
% @item
% The rows of @var{Hn} are orthogonal.
% @item
% @code{det (@var{A}) <= abs(det (@var{Hn}))} for all @var{A} with
% @code{abs (@var{A} (@var{i}, @var{j})) <= 1}.
% @item
% Multiply any row or column by -1 and still have a Hadamard matrix.
% @end itemize
%
% @end deftypefn

CROSS-REFERENCE INFORMATION ^

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