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 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

Spreadsheet

	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

See Also

• CHOLESKYFACTORIZATION
• CONFERENCE
• PASCAL

References

• LU Decomposition

• List of Main Z Functions

• Z3 home