Manuals/calci/PERMUTATION

MATRIX("PERMUTATION",order)

• $order$ 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 $AA^{T}=I$, where $A^{T}$ is a transpose and I is the identity matrix.
• Permutation matrices are orthogonal .Hence, their inverse is their transpose: $P^{-1}=P^{T}$.
• 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).$_(SUM) = 18
• 3.MATRIX("permutation",5).$$$(SUM) =

1

1

1

1

1

• 4.MATRIX("permutation",5).$$(SUM) =

1

1

1

1

1

See Also

• ANTIDIAGONAL
• CONFERENCE
• PASCAL
• HANKEL