/// <summary>
/// The method works by using Gaussian elimination to covert the matrix A to a upper triangular matrix, U, and computes the
/// determinant as the product_i(U_ii) * (-1)^c, where c is the number of row exchange operations that coverts A to U
/// </summary>
/// <param name="A">The matrix for which to calculate determinant</param>
/// <returns>The determinant of A</returns>
public static double GetDeterminant(IMatrix A)
{
int colCount = A.ColCount;
int rowCount = A.RowCount;
Debug.Assert(colCount == rowCount);
double det = 1;
int rowExchangeOpCount = 0;
IMatrix C = GaussianElimination.GetEchelonForm(A, out rowExchangeOpCount);
foreach (int c in C.ColKeys)
{
det *= C[c, c];
}
return(det * (rowExchangeOpCount % 2 == 0 ? 1 : -1));
}
public RowSpace(IMatrix A)
{
int numRowExOperations = 0;
mEchelonA = GaussianElimination.GetEchelonForm(A, out mM, out numRowExOperations);
}