In linear algebra, the Crout matrix decomposition is an LU decomposition which decomposes a matrix into a lower triangular matrix (L), an upper triangular matrix (U) and, although not always needed, a permutation matrix (P).
The Crout matrix decomposition algorithm differs slightly from the Doolittle method. Doolittle's method returns a unit lower triangular matrix and a upper triangular matrix where the Crout method returns a lower triangular matrix and a unit upper triangular matrix.
So, if a matrix decomposition of a matrix A is such that:
- A = LDU
being L an unit lower triangular matrix, D a diagonal matrix and U an unit upper triangular matrix, then Doolitle's method produces
- A = L(DU)
and Crout's method produces
- A = (LD)U.