Lower-Upper (LU) Decomposition.
Decompose (factorize) a square matrix A, whose dimension is n×n into components L and U, such that A = L × U, where
Decompose (factorize) a square matrix A, whose dimension is n×n into components L and U, such that A = L × U, where
- Matrix U is an upper triangular matrix (all the elements below the main diagonal are 0). Its dimension is n×n.
- Matrix L is a lower triangular matrix (all the elements above the main diagonal are 0), with all the elements on the main diagonal equal to 1.
By setting the diagonal to be all 1s, we are choosing the Doolittle decomposition. The dimension of L is n×n. - Please note that not every Matrix has the LU decomposition. However, if the matrix A is invertible, then there exists a permutation of its
rows P (permutation matrix), such that that the permuted matrix has LU decomposition: PA = LU . (or A = P-1LU)
Dimension n×n of the matrix : n =
A =
We are working hard to finish it, and you will be able to use it soon.
We are working hard to finish it, and you will be able to use it soon.