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hadamard

Hadamard matrix

Syntax

H = hadamard(n)

Description

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

Definitions

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

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Compute Hadamard Matrix

Compute the 4-by-4 Hadamard matrix.

H = hadamard(4)
H =

     1     1     1     1
     1    -1     1    -1
     1     1    -1    -1
     1    -1    -1     1

References

[1] Ryser, H. J., Combinatorial Mathematics, John Wiley and Sons, 1963.

[2] Pratt, W. K., Digital Signal Processing, John Wiley and Sons, 1978.

See Also

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Introduced before R2006a

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