Difference between revisions of "Manuals/calci/PERMUTATION"
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*2.MATRIX("permutation",18).$_(SUM) = 18 | *2.MATRIX("permutation",18).$_(SUM) = 18 | ||
| − | *3.MATRIX("permutation",5).$$$(SUM) = | + | *3.MATRIX("permutation",5).<math>\$$$</math>(SUM)= |
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| − | *4.MATRIX("permutation",5).$$(SUM) = | + | *4.MATRIX("permutation",5).<math>\$$</math>(SUM) = |
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Revision as of 05:53, 6 May 2015
MATRIX("PERMUTATION",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 size of the Permutation matrix.
Description
- This function returns the matrix Permutation matrix of order 3.
- A permutation matrix is a square binary matrix obtained by permuting the rows of an nxn identity matrix according to some permutation of the numbers 1 to n.
- This matrix has exactly one entry 1 in each row and each column and 0's elsewhere.
- A permutation matrix is nonsingular, and its determiant + or -.
- Also permutation matrix A having the following properties 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 AA^T=I} , where is a transpose and I is the identity matrix.
- Permutation matrices are orthogonal .Hence, their inverse is their transpose: 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 P^{-1} = P^T} .
- A permutation matrix allows to exchange rows or columns of another via the matrix-matrix product.
- In calci MATRIX("permutation",4) gives the permutation matrix of order 4.
is a transpose and I is the identity matrix.Examples
- 1.MATRIX("permutation",5,200..210)
| 0 | 0 | 0 | 200 | 0 |
| 0 | 201 | 0 | 0 | 0 |
| 202 | 0 | 0 | 0 | 0 |
| 0 | 0 | 203 | 0 | 0 |
| 0 | 0 | 0 | 0 | 204 |
- 2.MATRIX("permutation",18).$_(SUM) = 18
- 3.MATRIX("permutation",5).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 \$$$} (SUM)=
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- 4.MATRIX("permutation",5).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 \$$} (SUM) =
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See Also