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

0.5

-0.5

Upper-triangular U

-6

Permutation P

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.