The Polynomial Toolbox for MATLAB - DCE FEL ČVUT v Praze

isunimod(U)
ans =
1
Also the adjoint matrix is defined as for constant matrices. The adjoint is a
polynomial matrix and may be computed by typing
adj(P)
ans =
1 - s - s^2 0 s - s^2 - s^3
s + s^2 -s -1 + s + s^2 + s^3
-1 - s 1 -s^2
Quite to the contrary, the inverse of a square polynomial matrix is usually not a
polynomial but a polynomial fraction
inv(P)
ans =
-1 + s + s^2 0 -s + s^2 + s^3
-s - s^2 s 1 - s - s^2 - s^3
1 + s -1 s^2
----------------------------------------
-1 + s + s^2
For more details, see Chapter 4, Polynomial matrix fractions.
The only cases do have polynomial inverse are unimodular matrices. In our example
inv(U)
ans =
Indeed,
U*inv(U)
ans =
1 -2 - s + s^2 -1 + s + s^2 - s^3
-1 3 + s - s^2 1 - 2s - s^2 + s^3
1 -2 + s^2 s - s^3
1.0000 0 0
0 1.0000 0
0 0 1.0000