LDU Decomposition Calculator
Factor a square matrix into the product of a unit lower triangular matrix, a diagonal matrix, and a unit upper triangular matrix. Shows every elimination step.
Input Matrix
×3
Examples
Result
Enter a square matrix and click Compute LDU
What is LDU?
The LDU decomposition factors a square matrix into the product where is unit lower triangular, is diagonal, and is unit upper triangular.
When does it exist?
The factorization exists when all leading principal minors of are nonzero, meaning no pivoting is needed during Gaussian elimination. For symmetric positive definite matrices, it always exists.
Applications
LDU is useful for solving systems of equations efficiently, computing determinants (product of diagonal entries of ), and is the basis for Cholesky decomposition of symmetric positive definite matrices.