In general, there is no unique matrix solution to the matrix equation

Even in the case of
parallel to ,
there are still multiple matrices that perform this transformation. For example,
given ,
all the following matrices satisfy the above equation:

Therefore, vector division cannot be uniquely defined in terms of matrices.

However, if the vectors are represented by complex numbers or quaternions, vector division can be uniquely defined using the usual rules of complex
division and quaternion algebra, respectively.