Difference between revisions of "Manuals/calci/LUDECOMPOSITION"
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*In <math>LUDECOMPOSITION (Matrix)</math>, <math>Matrix</math> is any square matrix. | *In <math>LUDECOMPOSITION (Matrix)</math>, <math>Matrix</math> 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. | *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. | + | *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. | *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. | *LU Decomposition is also called LU Factorization.Here given matrix is split in to lower triangular and Upper triangular matrix. | ||
Revision as of 06:59, 4 September 2017
- 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 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 Matrix}
is any square 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
1. LUDECOMPOSITION([4,3;6,3])
|
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 |