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 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 A^T}
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.
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).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) = 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)=
1
1
1
1
1
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) =
is the size of the Permutation matrix.