Question: Let $\displaystyle T$ be a normal operator on a finite-dimensional complex inner product space $\displaystyle V$. Consider spectral decomposition $\displaystyle T = \lambda_1 T_1 + ... + \lambda_k T_k$ and prove that $\displaystyle T$ is invertible if and only if $\displaystyle \lambda_i \neq 0$ for $\displaystyle i \leq i \leq k$.

Any pointers would be helpful - I am unable to begin currently.