# Linear Algebra: Geometric Interpretation of Self-Adjoint Operators

1. Homework Statement
I'm not interested in the proof of this statement, just its geometric meaning (if it has one):

Suppose $$T \in L(V)$$ is self-adjoint, $$\lambda \in$$ F, and $$\epsilon > 0$$. If there exists $$v \in V$$ such that $$||v|| = 1$$ and $$|| Tv - \lambda v || < \epsilon$$, then $$T$$ has an eigenvalue $$\lambda '$$ such that $$| \lambda - \lambda ' | < \epsilon$$.

2. Homework Equations
n/a

3. The Attempt at a Solution
I thought this was similar to the statement that a function f(x) converges to a certain value(?)