ARK>class Vector<T> { public Vector(int len) { ... } }

ARK>class Matrix<T> { public Matrix(int len1, int len2) { ... } }

ARK>class Quaternion<T> { public Quaternion(int len) { ... } }
ARK>

#include <array>
#include <iostream>
#include <numeric>
#include <type_traits>
#include <utility>

template <typename T, typename U>
using ProductType = decltype(std::declval<T>() * std::declval<U>());

template <size_t N, typename T = double>
using Vector = std::array<T,N>;

template <size_t N, typename T, typename U>
ProductType<T,U> dotproduct(const Vector<N, T>& t, const Vector<N, U>& u)
{
  return std::inner_product(t.begin(), t.end(), u.begin(), ProductType<T,U>());
}

int main()
{
  const Vector<3, short> v1 { 1, 2, 3 };
  const Vector<3, signed char> v2 { 1, 2, 3 };
  auto res = dotproduct(v1, v2);

  static_assert(std::is_same<int, decltype(res)>::value, "Unxpected return type");

  std::cout << res << std::endl;
}