[tex]

V_1+ V_2 = \mathbb{R}^N,\quad\quad \textrm{dim}(V_1)=2,\quad \textrm{dim}(V_2)=N-2

[/tex]

and such that the restriction of [itex]A[/itex] to [itex]V_1[/itex] belongs to [itex]\textrm{SO}(2)[/itex], and that the restriction of [itex]A[/itex] to [itex]V_2[/itex] is the identity [itex]1[/itex]?