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hadamard - Hadamard matrix

Syntax

H = hadamard(n)

Description

H = hadamard(n) returns the Hadamard matrix of order n.

Definition

Hadamard matrices are matrices of 1's and -1's whose columns are orthogonal,

H'*H = n*I

where [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 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

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.

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