Sep 1, 2025 · LU decomposition breaks a matrix into two simpler matrices: one with numbers below the diagonal (L) and one above the diagonal (U). This makes solving equations, finding inverses and …

In numerical analysis and linear algebra, lower–upper (LU) decomposition or factorization factors a matrix as the product of a lower triangular matrix and an upper triangular matrix (see matrix …

The calculator will find (if possible) the LU decomposition of the given matrix A A, i.e. such a lower triangular matrix L L and an upper triangular matrix U U that A = L U A = LU, with steps shown.

To appreciate why LU decomposition could be a better choice than the Gauss elimination techniques in some cases, let us discuss first what LU decomposition is about.

For two matrices LU, we can multiply one entire column of L by a constant and divide the corresponding row of U by the same constant without changing the product of the two matrices.

Examples to find the LU matrix decomposition are presented along with detailed solutions and questions with solutions.

Given a matrix A there are many different algorithms to find the matrices L and U for the LU decomposition. Here we will use the recursive leading-row-column LU algorithm.