Wie sieht eine schon brauchbare Vektorklasse aus?

Damit sieht unsere soweit fertige Vektorklasse wie folgt aus:

class CVector {
private:
  static double epsilon;
  static int    instances;
private:
  int     dimension;
  double *vector;
public:
  /* constructors and destructor */
   CVector(int dimension=3);
   CVector(const CVector& v);
  ~CVector();

  /* input and output */
  friend ostream& operator<<(
          ostream& os,
    const CVector& v
  );
  friend istream& operator>>(
    istream& is,
    CVector& v
  );

  /* some operators */
  CVector& operator=(const CVector& v);
  CVector  operator+(const CVector& v) const;
  CVector  operator-(const CVector& v) const;
  double   operator*(const CVector& v) const;
  CVector  operator+() const;
  CVector  operator-() const;
  CVector  operator!() const;
  CVector  operator*(double d) const;
  friend CVector operator*(
    const CVector& v,
          double   d
  );
  double&  operator[](int i) const;

  /* useful functions */
  int      Dimension() const;
  double   Length() const;
  bool     IsNullVector() const;
  CVector  SolvePolynom() const;

  /* control functions */
  void     SetEpsilon();
  void     GetEpsilon();
  void     GetInstances();
};