$\newcommand{\W}[1]{ \; #1 \; } \newcommand{\R}[1]{ {\rm #1} } \newcommand{\B}[1]{ {\bf #1} } \newcommand{\D}[2]{ \frac{\partial #1}{\partial #2} } \newcommand{\DD}[3]{ \frac{\partial^2 #1}{\partial #2 \partial #3} } \newcommand{\Dpow}[2]{ \frac{\partial^{#1}}{\partial {#2}^{#1}} } \newcommand{\dpow}[2]{ \frac{ {\rm d}^{#1}}{{\rm d}\, {#2}^{#1}} }$
Source: det_by_minor
# include <vector>

template <class Scalar>
class det_by_minor {
private:
size_t              m_;

// made mutable because modified and then restored
mutable std::vector<size_t> r_;
mutable std::vector<size_t> c_;

// make mutable because its value does not matter
mutable std::vector<Scalar> a_;
public:
det_by_minor(size_t m) : m_(m) , r_(m + 1) , c_(m + 1), a_(m * m)
{
size_t i;

// values for r and c that correspond to entire matrix
for(i = 0; i < m; i++)
{     r_[i] = i+1;
c_[i] = i+1;
}
r_[m] = 0;
c_[m] = 0;
}

template <class Vector>
inline Scalar operator()(const Vector &x) const
{     size_t i = m_ * m_;
while(i--)
a_[i] = x[i];
return det_of_minor(a_, m_, m_, r_, c_);
}

};