Solution
= Solution
The decomposition into $\operatorname{span}\{u\}$ and the zero-sum <vector subspace> gives <characteristic polynomial> $t^{n-1}(t-n)$. For $n\geq2$, \b[$n$ has <algebraic multiplicity> and <geometric multiplicity> one; zero has both multiplicities $n-1$]. At $n=1$, only the <eigenvalue> 1 occurs, with both multiplicities one. Referring to a multiplicity zero for the absent root zero is merely a bookkeeping convention, not an assertion that it is an <eigenvalue>.