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 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 or Hermitian and need not be positive definite. 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