Manuals/calci/LUDECOMPOSITION
- Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Matrix} is the set of values.
Description
- This function gives the value of LU Decomposition of a given matrix.
- In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle LUDECOMPOSITION (Matrix)} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Matrix} 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.
- LU Decomposition is also called LU Factorization.Here given matrix is split in to lower triangular and Upper triangular matrix.
For 2x2 matrix, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{bmatrix} a_{11} & a_{12} \\ a_{21}& a_{22} \end{bmatrix}=\begin{bmatrix} l_{11} & 0 \\ l_{21}& l_{22} \end{bmatrix}\begin{bmatrix} u_{11} & u_{12} \\ 0 & u_{22} \end{bmatrix}}
- For 3x3 matrix,
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21}& a_{22} & a_{23}\\ a_{31} & a_{32} & a_{33} \end{bmatrix}=\begin{bmatrix} l_{11} & 0 &0 \\ l_{21}& l_{22} &0 \\ l_{31}& l_{32} & l_{33} \end{bmatrix}\begin{bmatrix} u_{11} & u_{12} &u_{13} \\ 0 & u_{22} &u_{23} \\ 0 & 0 & u_{33} \end{bmatrix}}
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 |
2. LUDECOMPOSITION([[10,12,16],[-8,-4,15],[20,24,28]])
|
1 0 0 |
-0.4 1 0 | 0.5 0 1 |
|
20 24 28 |
0 5.600000000000001 26.200000000000003 |
0 0 2 |
|
0 0 1 |
0 1 0 |
1 0 0 |