I read today that for a vector space $V$ and any subspace $S$, all complements of $S$ in $V$ are isomorphic to $V/S$, and thus to each other.
I want to ask, is there a case where $V\cong W$ are isomorphic vector spaces, where $V=S\oplus A$ and $W=S\oplus B$, but $A$ and $B$ are not isomorphic? So complements in different vector spaces, albeit isomorphic ones, need not be isomorphic themselves? Thanks.