Manuals/calci/HADAMARD

MATRIX("HADAMARD",order)

• $order$ 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.Let H be a Hadamard matrix of order n.
• The transpose of H is closely related to its inverse.
• The equivalent definition for hadamard matrix is:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H H^{T} = n I_{n}}
  

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle I_{n}} is the n × n identity matrix and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle H^T} is the transpose of H.

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