## Types in MathNet.Numerics.LinearAlgebra.Factorization

Type LU<T>

Namespace MathNet.Numerics.LinearAlgebra.Factorization

Interfaces ISolver<T>

A class which encapsulates the functionality of an LU factorization.

For a matrix A, the LU factorization is a pair of lower triangular matrix L and upper triangular matrix U so that A = L*U.

In the Math.NET implementation we also store a set of pivot elements for increased numerical stability. The pivot elements encode a permutation matrix P such that P*A = L*U.

The computation of the LU factorization is done at construction time.

### Public Methods

#### Matrix<T>Inverse()

Returns the inverse of this matrix. The inverse is calculated using LU decomposition.
##### Return
###### `Matrix<T>`

The inverse of this matrix.

#### Matrix<T>Solve(Matrix<T> input)

Solves a system of linear equations, , with A LU factorized.
##### Parameters
###### `Matrix<T>` input

The right hand side Matrix`1 , .

##### Return
###### `Matrix<T>`

The left hand side Matrix`1 , .

#### voidSolve(Matrix<T> input, Matrix<T> result)

Solves a system of linear equations, , with A LU factorized.
##### Parameters
###### `Matrix<T>` input

The right hand side Matrix`1 , .

###### `Matrix<T>` result

The left hand side Matrix`1 , .

#### Vector<T>Solve(Vector<T> input)

Solves a system of linear equations, , with A LU factorized.
##### Parameters
###### `Vector<T>` input

The right hand side vector, .

##### Return
###### `Vector<T>`

The left hand side Vector`1 , .

#### voidSolve(Vector<T> input, Vector<T> result)

Solves a system of linear equations, , with A LU factorized.
##### Parameters
###### `Vector<T>` input

The right hand side vector, .

###### `Vector<T>` result

The left hand side Matrix`1 , .

### Public Properties

#### TDeterminant get;

Gets the determinant of the matrix for which the LU factorization was computed.

#### Matrix<T>L get;

Gets the lower triangular factor.

#### PermutationP get;

Gets the permutation applied to LU factorization.

#### Matrix<T>U get;

Gets the upper triangular factor.