12.1

Question 1

Let $A=PDP^{-1}$ be the diagonalization of $A$. What is $D$ equal to ?

Question 2

Let $f$ be a linear transformation. What is the associated matrix in the eigenvector basis of $f$ ?

$$\begin{equation*} f \colon \, \mathbb{R}^2 \to \mathbb{R}^2 \\ \quad \vec{x} \mapsto \begin{pmatrix} -1 & -4 \\ -2 & 1 \end{pmatrix} \vec{x} \end{equation*}$$