GeneralizedSchurDecomposition<T> Class

public abstract class GeneralizedSchurDecomposition<T> : GeneralizedDecomposition<T>

Public MustInherit Class GeneralizedSchurDecomposition(Of T)
	Inherits GeneralizedDecomposition(Of T)

generic<typename T>
public ref class GeneralizedSchurDecomposition abstract : public GeneralizedDecomposition<T>

[<AbstractClassAttribute>]
type GeneralizedSchurDecomposition<'T> = 
    class
        inherit GeneralizedDecomposition<'T>
    end

Inheritance

Object  →  GeneralizedDecomposition<T>  →  GeneralizedSchurDecomposition<T>

Derived

Numerics.NET.LinearAlgebra.ComplexDenseGeneralizedSchurDecomposition<T>

Type Parameters

T

The generalized Schur decomposition or QZ decomposition of a pair of square matrices A and B computes orthogonal (unitary) matrices, Q and Z, so that

A = QSZ^* and B = QTZ^*.

where S and T are upper triangular matrices.

The matrices S and T are called the Schur forms of A and B, respectively. The rows of the matrices Q and Z are called the left and right Schur vectors.

The generalized eigenvalues of A and B are the ratios of corresponding diagonal elements of S and T.

For a real matrix, the generalized eigenvalues are either real or come in complex conjugate pairs. When there are complex eigenvalues, the matrix S is modified to be quasi-triangular, where 2x2 blocks on the diagonal correspond to the complex eigenvalues. This is called the real Schur form. The matrix T is always upper triangular.

GeneralizedSchurDecomposition<T> inherits fromGeneralizedDecomposition<T>.

Reference