SymmetricIndefiniteDecomposition<T> Class

public abstract class SymmetricIndefiniteDecomposition<T> : Decomposition<T>

Public MustInherit Class SymmetricIndefiniteDecomposition(Of T)
	Inherits Decomposition(Of T)

generic<typename T>
public ref class SymmetricIndefiniteDecomposition abstract : public Decomposition<T>

[<AbstractClassAttribute>]
type SymmetricIndefiniteDecomposition<'T> = 
    class
        inherit Decomposition<'T>
    end

Inheritance

Object  →  LinearOperator<T>  →  Decomposition<T>  →  SymmetricIndefiniteDecomposition<T>

Type Parameters

T

The Bunch-Kaufman decomposition of a real symmetric positive definite matrix A rewrites the matrix in the form A= LDL^T or A= UDU^T, where L is a unit lower triangular matrix, U is an unit upper triangular matrix, and D is a block diagonal matrix made up of 1x1 and 2x2 blocks.

SymmetricIndefiniteDecomposition<T> can operate in two modes. In overwrite mode, the original matrix is overwritten with the result of the decomposition. In preserve mode, the original matrix is preserved, and a new matrix is created to hold the decomposition. You can set the mode through the Overwrite property.

SymmetricIndefiniteDecomposition<T> inherits from LinearOperator<T>. This means you can use it to solve systems of linear equations where the matrix of the system is symmetric but not necessarily. You can solve for a single right-hand side, or for multiple right-hand sides using the Solve(Vector<T>) method. You can also calculate the determinant the inverse, and an estimate for the condition number.

To solve a symmetric positive definite system of equations, you can use the CholeskyDecomposition<T> class instead.

Reference