# 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 

LU Decomposition