If [itex]N>2[/itex] and [itex]A\in\textrm{SO}(N)[/itex] are arbitrary, does there exist subspaces [itex]V_1,V_2\subset\mathbb{R}^N[/itex] such that(adsbygoogle = window.adsbygoogle || []).push({});

[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]?

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# Restriction of SO(N) to 2 dim subspaces

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