# Talk:Invariant subspace

Hello,

I have a question related to the article on invariant subspaces. So, Let V and U be subspaces of W such that W is the orthogonal sum of U and V. Let T be a linear mapping such that T: V -> V and T: U -> U. Accordingly, we can say that V and U are both invariant subspaces of T (or that U and V are T-invariant subspaces). What about if I have a mapping S: V -> U and S: U -> V. Is there a technical name for this? I would appreciate if you can point out some literature on the subject.

Tank you very much.

193.136.189.2 (talk) 11:00, 9 April 2009 (UTC)MR

in the case S, in addition to S: V -> U and S: U -> V, satisfies S^2 = I, it looks like you have something similar to a Z_2 grading on W. Mct mht (talk) 22:35, 9 April 2009 (UTC)

Thank you for your reply Mct. No, it does not happen in my case. I would say, if I was allowed, that U and V are "S-cross" and T-invariant subspaces with respect to W (or something like that) but I would be sloppy. My point is that T-invariance is important and has a name that we can employ and everyone will know what it is. Unfortunately, "S-cross" is also important for me but I search and don't find a name for it, that is why I am being "sloppy" and call it, by now, "S-cross" invariance with respect to W. Thanks for your time. 85.247.86.194 (talk)MR

Just a curiosity: V and U will be invariant subspaces of S^2 right? MAC 160.39.248.110 (talk) 01:54, 20 May 2014 (UTC)