## Types in MathNet.Numerics.LinearAlgebra.Factorization

Type QR<T>

Namespace MathNet.Numerics.LinearAlgebra.Factorization

Interfaces ISolver<T>

A class which encapsulates the functionality of the QR decomposition.

Any real square matrix A (m x n) may be decomposed as A = QR where Q is an orthogonal matrix (its columns are orthogonal unit vectors meaning QTQ = I) and R is an upper triangular matrix (also called right triangular matrix).

The computation of the QR decomposition is done at construction time by Householder transformation. If a factorization is performed, the resulting Q matrix is an m x m matrix and the R matrix is an m x n matrix. If a factorization is performed, the resulting Q matrix is an m x n matrix and the R matrix is an n x n matrix.

### Public Methods

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

Solves a system of linear equations, , with A QR 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 QR 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 QR 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 QR 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 absolute determinant value of the matrix for which the QR matrix was computed.

#### boolIsFullRank get;

Gets a value indicating whether the matrix is full rank or not.
Value:

#### Matrix<T>Q get;

Gets or sets orthogonal Q matrix

#### Matrix<T>R get;

Gets the upper triangular factor R.