Manuals/calci/LUDECOMPOSITION

LUDECOMPOSITION (Matrix)

• $Matrix$ is the set of values.

Description

• This function gives the value of LU Decomposition of a given matrix.
• In $LUDECOMPOSITION(Matrix)$, $Matrix$ 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,

\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_{21} & u_{12} \\ 0 & u_{22} \end{bmatrix}

• For 3x3 matrix,