Difference between revisions of "Manuals/calci/PERMUTATION"

Revision as of 12:50, 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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 *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.
+*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.