I'm not interested in the proof of this statement, just its geometric meaning (if it has one):
Suppose [tex] T \in L(V) [/tex] is self-adjoint, [tex]\lambda \in[/tex] F, and [tex]\epsilon > 0[/tex]. If there exists [tex]v \in V[/tex] such that [tex]||v|| = 1 [/tex] and [tex] || Tv - \lambda v || < \epsilon[/tex], then [tex]T[/tex] has an eigenvalue [tex]\lambda '[/tex] such that [tex]| \lambda - \lambda ' | < \epsilon[/tex].
The Attempt at a Solution
I thought this was similar to the statement that a function f(x) converges to a certain value(?)