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*A permutation matrix is nonsingular, and its determiant + or -.
*A permutation matrix is nonsingular, and its determiant + or -.
*Also permutation matrix A having the following properties <math>AA^T=I</math>, where <math>A^T</math> is a transpose and I is the identity matrix.
*Also permutation matrix A having the following properties <math>AA^T=I</math>, where <math>A^T</math> is a transpose and I is the identity matrix.
*Permutation matrices are orthogonal (hence, their inverse is their transpose: <math>P^{-1} = P^T</math>).
*Permutation matrices are orthogonal .Hence, their inverse is their transpose: <math>P^{-1} = P^T</math>.
*A permutation matrix allows to exchange rows or columns of another via the matrix-matrix product.
*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.
*In calci MATRIX("permutation",4) gives the permutation matrix of order 4.
==Examples==
*1.MATRIX("permutation",5,200..210)
{| class="wikitable"
|-
| 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).$$$(SUM)
{| class="wikitable"
|-
| 1
|-
| 1
|-
| 1
|-
| 1
|-
| 1
|}
*4.MATRIX("permutation",5).$$(SUM)
{| class="wikitable"
|-
| 1
|-
| 1
|-
| 1
|-
| 1
|-
| 1
|}
==See Also==
*[[Manuals/calci/ANTIDIAGONAL| ANTIDIAGONAL]]
*[[Manuals/calci/CONFERENCE| CONFERENCE]]
*[[Manuals/calci/PASCAL| PASCAL]]
*[[Manuals/calci/HANKEL| HANKEL]]
==References==