# Manuals/calci/PERMUTATION

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

## Related Videos

Permutation Matrix