Orthogonal projection onto a line

#linear_algebra

Let $T : R^{3} \to R^{3}$ be the orthogonal projection to a $1$ -dimensional linear subspace $L \subset R^{3}$ .
(a) List the eigenvalues of $T$ .
(b) Write the characteristic polynomial $p_{T} (x)$ for $T$ .
(c) Is $T$ diagonalizable? Briefly justify your answer.

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Let $T:{\bf R}^3\to {\bf R}^3$ be the orthogonal projection to a $1$-dimensional linear subspace $L\subset {\bf R}^3$.
\begin{enumerate}[label=\alph*)]
	\item List the eigenvalues of $T$.
	\item Write the characteristic polynomial $p_T(x)$ for $T$.
	\item Is $T$ diagonalizable? Briefly justify your answer.
\end{enumerate}