# 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 |