MATLAB Functions | Help Desk |
hadamard
Hadamard matrix
H = hadamard(n)
H = hadamard(n)
returns the Hadamard matrix of order n
.
Hadamard matrices are matrices of 1
's and -1
's whose columns are orthogonal,
H'*H = n*Iwhere
[n
n]
=
size(H)
and I
=
eye(n
,n)
.
They have applications in several different areas, including combinatorics, signal processing, and numerical analysis, [1], [2].
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.
The command hadamard(4)
produces the 4-by-4 matrix:
1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 1
compan
Companion matrix
hankel
Hankel matrix
toeplitz
Toeplitz matrix