Orthogonal projection onto a line (2)
Let
- List the eigenvalues of
. - Write the characteristic polynomial
for . - Is
diagonalizable? 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? Justify your answer.
\end{enumerate}