determinant.cpp

template <typename size_t N>
double determinant_nxn(const MatrixXd& m)
{
	if (m.cols() != m.rows())
	{
		cout << "Matrix must be " << N << "x" << N << endl;
		return 0;
	}

	Vector_nD<N> a_nd;
	
	for (size_t i = 0; i < N; i++)
		a_nd.components[i] = m(0, i);

	std::vector<Vector_nD<N>> vectors;

	for (size_t i = 1; i < N; i++)
	{
		Vector_nD<N> non;

		for (size_t j = 0; j < N; j++)
			non.components[j] = m(i, j);

		vectors.push_back(non);
	}

	// Compute the cross product
	Vector_nD<N> result = Vector_nD<N>::cross_product(vectors);

	for (size_t i = 0; i < result.components.size(); i++)
		if (i % 2 == 1)
			result.components[i] = -result.components[i];

	double d_dot = Vector_nD<N>::dot_product(a_nd, result);
	
	cout << d_dot << endl;
	cout << m.determinant() << endl << endl;

	return d_dot;
}

... and ...

int main(int argc, char** argv)
{
	cout << std::scientific << endl;
	//	cout << setprecision(20) << endl;

	const size_t N = 10;

	MatrixXd m(N, N);

	for (size_t i = 0; i < N; i++)
		for (size_t j = 0; j < N; j++)
			m(i, j) = static_cast<double>(rand());

	determinant_nxn<N>(m);

	return 0;
}