Difference between revisions of "Manuals/calci/PERMUTATION"

Revision as of 13:49, 30 April 2015

MATRIX("PERMUTATION",order)

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.

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-<div style="font-size:30px">'''PERMUTATION'''</div><br/>
+<div style="font-size:30px">'''MATRIX("PERMUTATION",order)'''</div><br/>
+*<math>order</math> 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 <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>).
+*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.