In control theory, we may need to find out whether or not a system such as x ˙ = A x + B u y = C x + D u {\displaystyle {\begin{array}{c}{\dot {\boldsymbol {x}}}{\boldsymbol {=Ax}}+{\boldsymbol {Bu}}\\{\boldsymbol {y}}={\boldsymbol {Cx}}+{\boldsymbol {Du}}\end{array}}} is controllable, where A {\displaystyle {\boldsymbol {A}}}, B {\displaystyle {\boldsymbol {B}}}, C {\displaystyle {\boldsymbol {C}}} and D {\displaystyle {\boldsymbol {D}}} are, respectively, n × n {\displaystyle n\times n}, n × p {\displaystyle n\times p}, q × n {\displaystyle q\times n} and q × p {\displaystyle q\times p} matrices. Wikipedia