How to find invariant subspaces under the transformation?
let say the matrix
$$A= \left[\begin{matrix}1&0&1&-1\2&1&2&1\0&1&6&1\3&1&3&4\end{matrix}\right]$$
when M is set of vectors of the form $0,\alpha,\beta, \beta$

Question

How to find invariant subspaces under the transformation?
let say the matrix 
$$A= \left[\begin{matrix}1&0&1&-1\2&1&2&1\0&1&6&1\3&1&3&4\end{matrix}\right]$$
when M is set of vectors of the form $0,\alpha,\beta, \beta$

loser66 · Answer

@KingGeorge

loser66 · Answer

@zzr0ck3r

loser66 · Answer

I know $A_0~~and~~A_4$ are 2 of them, but not sure how to find $A_1,~A_2~,~A_3$

kinggeorge · Answer

To be totally honest, I'm not really sure on how to find all invariant subspaces. What are $A_0$ and $A_4$?