I am confused about state-space reduction. I learned it in the class but am not skilled in it.
If $A,B,C,D$ matrices are given with values, we can
1. find its controllability matrix to see if controllable, if uncontrollable
2. find a transformation matrix $P$
3. reduce the state space to a controllable state space representation
However, if NOT given values, just like the following:
Can I reduce the above state space representation to the following: