54 The transfer function of $(A,B,C,D)$ (see also 92)

The transfer function of $(A,B,C,D)$ is

If $sI-A$ is invertible, then the following block matrices are row equivalent over $𝐂(s)$:

We observe that $T(s)$ can be computed exactly by matrix multiplication and elementary row operations. The next results tell us about $T(s)$.