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 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 AA^(T)=I} , 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.