Original sentence: For the case of column vector c and row vector r, the formula allows the quick calculation of the determinant of a matrix that differs from the identity matrix by a matrix of rank 1:
Edited sentence: For the case of column vector c and row vector r, each with m components, the formula allows the quick calculation of the determinant of a matrix that differs from the identity matrix by a matrix of rank 1:.where  and  are the m-by-m and n-by-n identity matrices, respectively