Manuals/calci/LUDECOMPOSITION

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LUDECOMPOSITION (Matrix)


  • is the set of values.

Description

  • This function gives the value of LU Decomposition of a given matrix.
  • In  ,   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,

 

  • For 3x3 matrix,

 

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
Spreadsheet
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

Related Videos

LU Decomposition

See Also

References