Difference between revisions of "Manuals/calci/LUDECOMPOSITION"
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*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(PA=LU). |
*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. | ||
**For 2x2 matrix, | **For 2x2 matrix, | ||
Line 48: | Line 48: | ||
|} | |} | ||
=LUDECOMPOSITION(A1:B2) | =LUDECOMPOSITION(A1:B2) | ||
− | {| border="1" cellpadding=" | + | {| border="1" cellpadding="5" cellspacing="0" |
|- | |- | ||
| | | | ||
− | 1 | + | 1 0 |
|| | || | ||
− | 0.6666666666666666 1 | + | 0.6666666666666666 1 |
|- | |- | ||
| | | | ||
− | 6 | + | 6 3 |
|| | || | ||
0 1 | 0 1 | ||
Line 65: | Line 65: | ||
1 0 | 1 0 | ||
|} | |} | ||
− | 2 | + | |
+ | {| class="wikitable" | ||
+ | |+Spreadsheet | ||
+ | |- | ||
+ | ! !! A !! B !! C | ||
+ | |- | ||
+ | ! 1 | ||
+ | | 1 || 2 || 3 | ||
+ | |- | ||
+ | ! 2 | ||
+ | | 4 || 5 || 6 | ||
+ | |- | ||
+ | ! 3 | ||
+ | | 7 || 8 || 9 | ||
+ | |} | ||
+ | =LUDECOMPOSITION(A1:C3) | ||
{| border="1" cellpadding="5" cellspacing="0" | {| border="1" cellpadding="5" cellspacing="0" | ||
|- | |- | ||
| | | | ||
− | 1 | + | 1 0 0 |
− | | | + | || |
− | | 0. | + | 0.5714285714285714 1 0 |
+ | || | ||
+ | 0.14285714285714285 1.999999999999999 1 | ||
|- | |- | ||
| | | | ||
− | + | 7 8 9 | |
− | | | + | || |
− | 0 | + | 0 0.4285714285714288 0.8571428571428577 |
− | | | + | || |
− | 0 0 | + | 0 0 0 |
|- | |- | ||
| | | | ||
− | 0 0 1 | + | 0 0 1 |
− | | | + | || |
− | 0 | + | 0 1 0 |
− | | | + | || |
− | 1 | + | 1 0 0 |
|} | |} | ||
+ | |||
+ | ==Related Videos== | ||
+ | |||
+ | {{#ev:youtube|v=UlWcofkUDDU|280|center|LU Decomposition}} | ||
==See Also== | ==See Also== |
Latest revision as of 13:30, 29 April 2019
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
A | B | |
---|---|---|
1 | 4 | 3 |
2 | 6 | 3 |
=LUDECOMPOSITION(A1:B2)
1 0 |
0.6666666666666666 1 |
6 3 |
0 1 |
0 1 |
1 0 |
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 |