public static int Rank(MMatrix A)
{
MMatrix temp = A.EchelonForm();
int index = Math.Min(temp.row, temp.col);
int rank = 0;
for (int i = 0; i < index; ++i)
{
if (temp[i, i] != 0)
rank++;
}
return rank;
}
//Homogenious system: Solve A*x = 0
public static Vector SolveSystemOfEquations(MMatrix A)
{
MMatrix Ref = new MMatrix();
Vector x = new Vector(A.col);
double sum;
Ref = A.EchelonForm();
for (int i = A.row - 1; i >= 0; i--)
{
//The system has more than one solutions. Get one.
if (Ref[i, i] == 0)
x[i] = 1;
else
{
sum = 0;
for (int j = i + 1; j < Ref.col; ++j)
{
sum += Ref[i, j] * x[j];
}
x[i] = -sum / Ref[i, i];
}
}
return x;
}