LU Decomposition Calculator
Decompose matrix A into L (lower triangular) and U (upper triangular) such that A = LU.
Matrix A
A = LU
Decomposition Successful
det(A) = 4.000000
L (Lower Triangular)
1.0000.0000.000
2.0001.0000.000
4.0003.0001.000
U (Upper Triangular)
2.0001.0001.000
0.0001.0001.000
0.0000.0002.000
Verification: L × U
2.0001.0001.000
4.0003.0003.000
8.0007.0009.000
Multipliers (L entries)
L[2][1] = 2.0000
L[3][1] = 4.0000
L[3][2] = 3.0000
LU Decomposition
Properties
- L has 1s on diagonal, zeros above
- U has zeros below diagonal
- det(A) = det(L) × det(U) = product of U diagonal
Applications
- Solving linear systems Ax = b
- Computing determinants efficiently
- Matrix inversion