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Determinant


Functions

double itpp::det (const mat &X)
 Determinant of real square matrix.
std::complex< double > itpp::det (const cmat &X)
 Determinant of complex square matrix.

Detailed Description


Function Documentation

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$ dependening on the number of row permuations

Definition at line 46 of file det.cpp.

References it_assert1, and itpp::lu().

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$ dependening on the number of row permuations

Definition at line 79 of file det.cpp.

References it_assert1, and itpp::lu().

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