can be solved, for example, by rewriting it as a matrix equation \mathbf{X} = \mathbf{A} \, \mathbf{Y} where matrices \mathbf{X} and \mathbf{Y} contain the vectors \mathbf{x}_{k} and \mathbf{y}_{k} in their respective columns.
Solutions can also be described in the case that the equations are over or under determined.