Difference between revisions of "Manuals/calci/HADAMARD"
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==Examples== | ==Examples== | ||
| − | + | *1.MATRIX("hadamard") = 1 | |
| − | + | *2.MATRIX("hadamard",3) | |
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|1 || -1 ||-1 || 1 | |1 || -1 ||-1 || 1 | ||
|} | |} | ||
| − | + | *3.MATRIX("hadamard",4) | |
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
Revision as of 01:02, 26 October 2015
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 (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_1=\begin{bmatrix} 1 \\ \end{bmatrix}}
- 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_2 = \begin{bmatrix} 1 & 1 \\ 1 & -1 \\ \end{bmatrix}}
- 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_3 =\begin{bmatrix} 1 & 1 & 1 & 1 \\ 1 & -1 & 1 & -1\\ 1 & 1 & -1 & -1 \\ 1 & -1 & -1 & 1\\ \end{bmatrix}}
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 |