AI engineering glossary · Linear algebra
What is LU decomposition?
LU decomposition (also called LU factorisation): A factorisation of a square matrix into a lower triangular matrix L and an upper triangular matrix U, usually with row swaps. Once done, many systems with the same matrix and different right sides are solved fast by two triangular solves.
LU decomposition: an example
A = L U lets you solve A x = b by first solving L y = b and then U x = y.
Related terms
More Linear algebra terms
- Matrix
- Matrix multiplication
- Matrix norm
- Matrix-vector product
- Norm
- Normal equations
- Null space
- Orthogonal matrix
Where you learn it
LU decomposition is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.