H = hadamard(n)
hadamard(n)
returns the Hadamard matrix of order n
.Hadamard matrices have applications in several different areas, including combinatorics, signal processing, and numerical analysis, [1], [2]. They are matrices of 1s and -1s whose columns are orthogonal,
H'*H = n*I
where [n n] = size(H)
and I = eye(n
,n)
.
An n
-by-n
Hadamard matrix with n > 2
exists only if rem(n,4) = 0
. This function handles only the cases where n
, n/12
, or n/20
is a power of 2.
hadamard(4)
is the 4-by-4 matrix
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
contour(hadamard(32))
is a plot reminiscent of a Navajo rug.
compan
,hankel
,toeplitz
[2] W. K. Pratt, Digital Signal Processing, John Wiley and Sons, 1978.
(c) Copyright 1994 by The MathWorks, Inc.