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Image_Processing_Tool_2 >> Image_Processing_Tool_2 > hadamard

hadamard

Generate the hadamard matrix

Calling Sequence

Had_Mat = hadamard(N)

Arguments

Had_Mat

A square matrix having the values 1 and -1.

N

row/column value of the output matrix.

Description

The name derives from a theorem of Hadamard. The columns of the hadamard matrices are orthogonal. The mathematical expression of being orthogonality of a matrix is given below: Had_Mat'*Had_Mat = n*eye(n,n); Where, [n, n] = size(Had_Mat); Here n must be greater than or equal to 2 and modulo(n, 4) should be equal to zero (0). One important feature of the hadamard matrix is the sequency value for each row. The sequency value is the number of change of sign in each row. The smallest order for which a Hadamard matrix has not been constructed is 268.

Examples

B = hadamard(4);

It produces a 4-by-4 hadamard matrix as given below:

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

Research in the area of Hadamard matrices and their applications has steadily and rapidly grown, specially during the last three decades. These matrices can be transformed to produce incomplete block designs, t-designs, orthogonal F-square designs, error correcting and detecting codes, Walsh functions and other mathematical and statistical objects.

See Also

Authors

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