Difference between revisions of "Manuals/calci/HADAMARD"
Jump to navigation
Jump to search
(Created page with "<div style="font-size:30px">'''HADAMARD'''</div><br/>") |
|||
| Line 1: | Line 1: | ||
| − | <div style="font-size:30px">'''HADAMARD'''</div><br/> | + | <div style="font-size:30px">'''MATRIX("HADAMARD",order)'''</div><br/> |
| + | *<math>order</math> 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: | ||
| + | <math>H H^{T} = n I_{n}</math> | ||
| + | where <math>I_{n}</math> is the n × n identity matrix and <math>H^T</math> 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: | ||
Revision as of 13:29, 23 April 2015
MATRIX("HADAMARD",order)
- is the order of the hadamard 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.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: