LU Decomposition
Factor a matrix as L U with partial pivoting
Doolittle with partial pivoting: P · A = L · U, det(A) = (−1)^swaps × ∏ diag(U)
Determinant
-16
Row swaps
1 · row order: 2 · 1 · 3
Lower-triangular L
1
0
0
0.5
1
0
-0.5
1
1
Upper-triangular U
4
-6
0
0
4
1
0
0
1
Permutation P
0
1
0
1
0
0
0
0
1
L is unit lower-triangular (1s on the diagonal) and U is upper-triangular. Multiplying L · U reproduces the row-permuted matrix P · A, which confirms the factorization.