/sci/ - Science & Math

>>9024765
[math] ker(T^{n-2}) \leq V [/math] so it has a complement, i.e. [math] \exists V_2 \leq V [/math] such that [math] V_2\oplus ker(T^{n-2})=V [/math].
But [math] T(V_1) \cap ker(T^{n-2})=\{0\}[/math] so [math] T(V_1) \subset V_2 [/math], by the definition of the direct sum.