where λ = s or λ = z for a continuousor discrete-time realization, respectively. It is widely accepted that most numerical operations on rational or polynomial matrices are best done by manipulating the matrices of the corresponding descriptor system representations. Many operations on standard matrices (such as finding the rank, determinant, inverse or generalized inverses, nullspace) or the s...

We consider the set of quadruples of matrices defining singular linear time-invariant dynamical systems and show that there is a one-to-one correspondence between this set and a subset of the set of polynomial matrices of degree two. This correspondence preserves the equivalence relations introduced in both sets (feedback-similarity and strict equivalence): two quadruples of matrices are feedba...