Manuals/calci/LUDECOMPOSITION

LUDECOMPOSITION (Matrix)

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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,

${\begin{bmatrix}a_{11}&a_{12}&a_{13}\\a_{21}&a_{22}&a_{23}\\a_{31}&a_{32}&a_{33}\end{bmatrix}}={\begin{bmatrix}l_{11}&0&0\\l_{21}&l_{22}&0\\l_{31}&l_{32}&l_{33}\end{bmatrix}}{\begin{bmatrix}u_{11}&u_{12}&u_{13}\\0&u_{22}&u_{23}\\0&0&u_{33}\end{bmatrix}}$