Manuals/calci/PERMUTATION

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MATRIX("PERMUTATION",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 , where is a transpose and I is the identity matrix.
  • Permutation matrices are orthogonal .Hence, their inverse is their transpose: .
  • 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


References