To diagonalize our force-driven mass example, we may begin with its state-space model Eq.(1.9):
which is in the general state-space form as needed (Eq.(1.8)). We can see that is already a Jordan block of order 2 [452, p. 368]. (We can change the to 1 by scaling the physical units of .) Thus, the system is already as diagonal as it's going to get. We have a repeated pole at , and they are effectively in series (instead of parallel), thus giving a ``defective'' matrix [452, p. 136].