Manuals/calci/HADAMARD

MATRIX("HADAMARD",order)


  • 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 1 1 1
1 -1 1 -1
1 1 -1 -1
1 -1 -1 1
  1. 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

See Also

References