Manuals/calci/HADAMARD

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MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall)


  • is the type of the matrix.
  • is the order of the Hadamard matrix.

Description

  • This function gives the matrix satisfying the property of Hadamard.
  • A Hadamard matrix is the square matrix with the entries of 1 and -1.
  • Also the rows of that matrix are orthogonal.
  • So H be a Hadamard matrix of order 2n.
  • The transpose of H is closely related to its inverse.
  • The equivalent definition for hadamard matrix is:
  

where is the n × n identity matrix and is the transpose of H.

  • So the possible order of the matrix is 1,2 or positive multiple of 4.
  • The few examples of hadamard matrices are:

Examples

  • 1.MATRIX("hadamard") = 1
  • 2.MATRIX("hadamard",3)
1 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
  • 3.MATRIX("hadamard",4)
1 1 1 1 1 1 1 1
1 -1 1 -1 1 -1 1 -1
1 1 -1 -1 1 1 -1 -1
1 -1 -1 1 1 -1 -1 1
1 1 1 1 -1 -1 -1 -1
1 -1 1 -1 -1 1 -1 1
1 1 -1 -1 -1 -1 1 1
1 -1 -1 1 -1 1 1 -1

Related Videos

Numbers


See Also

References