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(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,
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 |
| 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 |