| MATLAB Function Reference | Search Help Desk |
| hadamard | Examples See Also |
Syntax
H = hadamard(n)
Description
H = hadamard(n)
returns the Hadamard matrix of order n.
Definition
Hadamard matrices are matrices of1'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.
Examples
The commandhadamard(4) produces the 4-by-4 matrix:
1 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 1
See Also
compan, hankel, toeplitz
References
[1] Ryser, H. J., Combinatorial Mathematics, John Wiley and Sons, 1963. [2] Pratt, W. K., Digital Signal Processing, John Wiley and Sons, 1978.