SingularValueDecomposition<T>.GetDeterminant Method

Calculates the determinant of the decomposed matrix.

Definition

Namespace: Extreme.Mathematics.LinearAlgebra
Assembly: Extreme.Numerics (in Extreme.Numerics.dll) Version: 8.1.23
C#
public override T GetDeterminant()

Return Value

T
The determinant of the matrix.

Remarks

A system of simultaneous linear equations has a unique solution if its determinant is not equal to zero.

Determinants are only defined for square matrices. If the matrix is not square, an exception of type DimensionMismatchException is thrown.

For a singular value decomposition A = USVT, the magnitude of the determinant is the product of the diagonal elements of S. Since U and V are orthogonal, their determinant is 1 or -1. This means that only the magnitude of the determinant is known, not its sign.

Exceptions

DimensionMismatchExceptionThe matrix is not square.

See Also