**Chapter
7. **** Solutions of Linear Systems** (.NET, C#, CSharp, VB, Visual Basic, F#)

**NMath** provides
classes for computing and storing the LU factorization for a matrix.

*LU factorization*
is a procedure for decomposing a matrix into a product of a *lower* triangular matrix and an *upper* triangular matrix. Given a matrix
A, an LU factorization class factors A as follows:

PA = LU

where P is a permutation matrix, L is a lower triangular matrix with ones on the diagonal, and U is an upper triangular matrix.

Once an LU factorization is constructed, it can be reused to solve for different right-hand sides, to compute inverses, to compute condition numbers, and so on.

**NMath**
also provides several static functions for solving linear systems, and
for computing determinants, inverses, and condition numbers.