Compute the determinant of a matrix.

gistfile1.cs

        /// <summary>
        /// Duplicates a ComplexMatrix without one columns and one row
        /// </summary>
        /// <param name="matrix"></param>
        /// <param name="column"></param>
        /// <param name="row"></param>
        /// <returns></returns>
        private Matrix make_matrix(Matrix matrix, int column)
        {
            Matrix new_matrix = new Matrix(matrix.Rows - 1, matrix.Columns - 1);

            ///2 Parts

            //1st
            for (int y = 0; y < column; y++)
            {
                for (int x = 1; x < matrix.Rows; x++)
                {
                    new_matrix[(x - 1), y] = matrix[x, y];
                }
            }
            //2nd
            for (int y = (column + 1); y < matrix.Columns; y++)
            {
                for (int x = 1; x < matrix.Rows; x++)
                {
                    new_matrix[(x - 1), (y - 1)] = matrix[x, y];
                }
            }

            return new_matrix;
        }

        //If the matrix is bigger then 2x2, det will be cast recursive until it is.
        private double det(Matrix matrix)
        {
            if (matrix.Rows != matrix.Columns)
            {
                throw new Exception("Determinants can only be computed from square matrices.");
            }
               
            if (matrix.Rows == 2 && matrix.Columns == 2)
            {
                return ((matrix[0, 0] * matrix[1, 1]) - (matrix[0, 1] * matrix[1, 0]));
            }

            //ComplexMatrix is bigger then 2x2

            double ret_det  = 0;                               
            bool negative = false;                              

            for (int i = 0; i < matrix.Columns; i++)      
            {
                Matrix smallMatrix = make_matrix(matrix, i);
                if (negative)                                 
                {
                    ret_det += (-1) * matrix[0, i] * det(smallMatrix);
                    negative = false;                          
                }
                else
                {
                    ret_det += matrix[0, i] * det(smallMatrix);
                    negative = true;
                }
            }
            return ret_det;
        }