# Difference between revisions of "Manuals/calci/ANTIDIAGONAL"

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==Description== | ==Description== | ||

*This function gives the matrix satisfying the anti diagonal properties. | *This function gives the matrix satisfying the anti diagonal properties. | ||

− | *An anti-diagonal matrix is a matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner <math>\nearrow</math>, known as the anti-diagonal. | + | *An anti-diagonal matrix is a matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner (<math>\nearrow</math>), known as the anti-diagonal. |

*So here we are getting all entries are 0 except from the opposite of main diagonal as 1. | *So here we are getting all entries are 0 except from the opposite of main diagonal as 1. | ||

*The properties of anti diagonal matrix are: | *The properties of anti diagonal matrix are: |

## Revision as of 09:49, 17 April 2015

**MATRIX("ANTI-DIAGONAL",order)**

- is the order of the Anti diagonal matrix.

## Description

- This function gives the matrix satisfying the anti diagonal properties.
- An anti-diagonal matrix is a matrix where all the entries are zero except those on the diagonal going from the lower left corner to the upper right corner (), known as the anti-diagonal.
- So here we are getting all entries are 0 except from the opposite of main diagonal as 1.
- The properties of anti diagonal matrix are:
- 1.The product of two anti-diagonal matrices is a diagonal matrix.
- 2. If A and D are n×n anti-diagonal and diagonal matrices, respectively, then AD,DA are anti-diagonal.
- 3.All anti-diagonal matrices are also persymmetric.
- Here MATRIX("anti-diagonal") displays the antidiagonal matrix of order 3.
- To display the different order of matrices then the syntax is MATRIX("anti-diagonal",5).

## Examples

- MATRIX("ANTI-DIAGONAL")

0 | 0 | 1 |

0 | 1 | 0 |

1 | 0 | 0 |

- MATRIX("anti-diagonal",4,200..204)

0 | 0 | 0 | 200 |

0 | 0 | 201 | 0 |

0 | 202 | 0 | 0 |

203 | 0 | 0 | 0 |

- MATRIX("anti-diagonal",3,-32.05)

0 | 0 | -32.05 |

0 | -32.05 | 0 |

-32.05 | 0 | 0 |