Manuals/calci/PERMUTATION
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MATRIX("PERMUTATION",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 , where is a transpose and I is the identity matrix.
- Permutation matrices are orthogonal .Hence, their inverse is their transpose: .
- 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.
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).(SUM)=
1 |
1 |
1 |
1 |
1 |
- 4.MATRIX("permutation",5).(SUM) =
1 |
1 |
1 |
1 |
1 |