Diagonalizability
Defn
A linear map \(T:V\rightarrow V\) is diagonalizable if there exists an order basis \(\beta\) for \(V\) st \([T]_\beta\) is a diagonal matrix
A matrix \(A\) is diagonalizable if \(L_A\) is diagonalizable
Eg
\(T(f)=f(x)+(x+1)f'(x)\)
\(\beta=\{1,x,x^2\}\)
\[[T]_\beta= \begin{bmatrix}
T(1) & T(x) & T(x^2)
\end{bmatrix} = \begin{bmatrix}1 & 1 & 0 \\0 & 2 & 2 \\0 & 0 & 3 \end{bmatrix} \]