MATRIX("HADAMARD",order)
- 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 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:
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 few examples of hadamard matrices are:
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle H_{1}={\begin{bmatrix}1\\\end{bmatrix}}*H_{2}={\begin{bmatrix}1&1\\1&-1\\\end{bmatrix}}*H_{3}={\begin{bmatrix}1&1&1&1\\1&-1&1&-1\\1&1&-1&-1\\1&-1&-1&1\\\end{bmatrix}}}