typedef vector < double > Trow;
typedef vector < Trow > Tmatrix;

template < class T > ostream &	// template to print any vector 
  operator << (ostream & os, vector < T > v) {
  for (int i = 0; i < v.size (); i++)
    os << " " << v[i];
  os << "\n";
  return os;
}

void readmatrix (istream & is, Tmatrix & m);  // read a matrix

Trow operator *(double a, Trow r);

Tmatrix operator *(double a, Tmatrix m);

Trow operator + (Trow r, const Trow & rr); 

Tmatrix operator +(Tmatrix mm, Tmatrix  m);

Trow operator * (const Tmatrix & m, const Trow & r);

double norm(Trow r);

Tmatrix idmatrix(int n);