LUDecomposition<T>.GetDeterminant Method

public override T GetDeterminant()

Public Overrides Function GetDeterminant As T

public:
virtual T GetDeterminant() override

abstract GetDeterminant : unit -> 'T 
override GetDeterminant : unit -> 'T 

Return Value

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 LU factorized matrix PA = LU, the determinant is the product of the diagonal elements of U. Since L is defined to be unit triangular, so the product of its diagonal elements equals 1.

Reference