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

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− | <div style="font-size: | + | <div style="font-size:25px">'''MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall)'''</div><br/> |

+ | *<math>TypeOfMatrix</math> is the type of the matrix. | ||

+ | *<math> DimensionsOfMatrix </math> 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 (<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. | ||

+ | *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. | ||

+ | *To display the different order of matrices then the syntax is MATRIX("anti-diagonal",5). | ||

+ | |||

+ | ==Examples== | ||

+ | *MATRIX("ANTI-DIAGONAL") = 1 | ||

+ | *MATRIX("ANTI-DIAGONAL",3) | ||

+ | {| class="wikitable" | ||

+ | |- | ||

+ | | 0 || 0 || 1 | ||

+ | |- | ||

+ | | 0 || 1 || 0 | ||

+ | |- | ||

+ | | 1 || 0 || 0 | ||

+ | |} | ||

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

+ | {| class="wikitable" | ||

+ | |- | ||

+ | | 0 || 0 || 0 || 200 | ||

+ | |- | ||

+ | | 0 || 0 || 201 || 0 | ||

+ | |- | ||

+ | | 0 || 202 || 0 || 0 | ||

+ | |- | ||

+ | | 203 || 0 || 0 || 0 | ||

+ | |} | ||

+ | *MATRIX("anti-diagonal",3,-32.05) | ||

+ | {| class="wikitable" | ||

+ | |- | ||

+ | | 0 || 0 || -32.05 | ||

+ | |- | ||

+ | | 0 || -32.05 || 0 | ||

+ | |- | ||

+ | | -32.05 || 0 || 0 | ||

+ | |} | ||

+ | |||

+ | ==See Also== | ||

+ | *[[Manuals/calci/ARROWHEAD| ARROWHEAD]] | ||

+ | *[[Manuals/calci/MATRIXOPERATORS| MATRIXOPERATORS]] | ||

+ | |||

+ | ==Related Videos== | ||

+ | |||

+ | {{#ev:youtube|v=wbVMXohzcQU|280|center|Diagonal Matrix}} | ||

+ | |||

+ | ==References== | ||

+ | *[http://en.wikipedia.org/wiki/Anti-diagonal_matrix Anti Diagonal] | ||

+ | |||

+ | |||

+ | |||

+ | *[[Z_API_Functions | List of Main Z Functions]] | ||

+ | |||

+ | *[[ Z3 | Z3 home ]] |

## Latest revision as of 14:30, 9 April 2019

**MATRIX (TypeOfMatrix,DimensionsOfMatrix,SeedValuesToUse,IJFunction,PreParameter,IsItInternalCall)**

- is the type of the matrix.
- 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.
- To display the different order of matrices then the syntax is MATRIX("anti-diagonal",5).

## Examples

- MATRIX("ANTI-DIAGONAL") = 1
- MATRIX("ANTI-DIAGONAL",3)

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 |

## See Also

## Related Videos

## References