Talk:Aufgaben:Problem 2
Shouldn't one use somewhere that \(U \neq \{0\},\ V\). I think this is given for a reason.
Beni (talk) 09:29, 28 July 2015 (CEST)
The way the questions are asked: (c) "invariant subspace" still includes the trivial invariant subspaces, and in (d) "the decomposition into invariant subspaces" again does not exclude the case that it is the trivial decomposition into \(V\) and \(\{0\}\). If the question would ask for a non trivial invariant subspace and a non trivial decomposition then you would have mention that this is the case, because...
Apart from that I don't think there are any steps that would require this to be mentioned, if \(\pi\) is either the zero map or the identity then everything should still work.
Carl (talk) 13:43, 28 July 2015 (CEST)
Ah I see. Thanks!
Beni (talk) 10:59, 29 July 2015 (CEST)
In c): Should we maybe point out, that the kernel of any endomorphism in V forms a subspace and it is enough to show the invariance? Or is that too obvious?
