# Manuals/calci/LUDECOMPOSITION

**LUDECOMPOSITION (Matrix)**

- is the set of values.

## Description

- This function gives the value of LU Decomposition of a given matrix.
- In , is any square matrix.
- LU Decomposition is the procedure for decomposing any square matrix in to a product of Lower Triangular matrix and Upper Triangular matrix.
- In LU Decomposition, L stands for Lower Triangular matrix and U stands for Upper Triangular matrix.
- So A=LU.But sometimes the product includes Permutation Matrix also(PA=LU).
- LU Decomposition is also called LU Factorization.Here given matrix is split in to lower triangular and Upper triangular matrix.
- For 2x2 matrix,

- For 3x3 matrix,

## Examples

A | B | |
---|---|---|

1 | 4 | 3 |

2 | 6 | 3 |

=LUDECOMPOSITION(A1:B2)

1 0 |
0.6666666666666666 1 |

6 3 |
0 1 |

0 1 |
1 0 |

A | B | C | |
---|---|---|---|

1 | 1 | 2 | 3 |

2 | 4 | 5 | 6 |

3 | 7 | 8 | 9 |

=LUDECOMPOSITION(A1:C3)

1 0 0 |
0.5714285714285714 1 0 |
0.14285714285714285 1.999999999999999 1 |

7 8 9 |
0 0.4285714285714288 0.8571428571428577 |
0 0 0 |

0 0 1 |
0 1 0 |
1 0 0 |