Determinant
[Linear Algebra]


Functions
double	itpp::det (const mat &X)
	Determinant of real square matrix. Calculate determinant of the real matrix $\mathbf{X}$ .
std::complex< double >	itpp::det (const cmat &X)
	Determinant of complex square matrix. Calculate determinant of the complex matrix $\mathbf{X}$ .

Function Documentation

std::complex< double > itpp::det ( const cmat & X )

Determinant of complex square matrix.

Calculate determinant of the complex matrix $\mathbf{X}$ .

Uses LU-factorisation.

$\det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U}))$

and the determinant of the permuation matrix is $\pm 1$ depending on the number of row permutations

double itpp::det ( const mat & X )

Determinant of real square matrix.

Calculate determinant of the real matrix $\mathbf{X}$ .

Uses LU-factorisation.

$\det(\mathbf{X}) = \det(\mathbf{P}^T \mathbf{L}) \det(\mathbf{U}) = \det(\mathbf{P}^T) \prod(\mathrm{diag}(\mathbf{U}))$

and the determinant of the permuation matrix is $\pm 1$ depending on the number of row permutations