Span of similar matrices Given $D=\begin{pmatrix} 3 & 0 \\ 0 & 2\\ \end{pmatrix}$
How can i find the span of all matrices A that are similar to D.
thus $\exists P$  $A=P^{-1}DP$

Here are four matrices similar to $D$ which span all of $\mathbb{R}^{2\times 2}$:
$$ \begin{pmatrix} 3 & 0 \\ 0 & 2 \end{pmatrix},
   \begin{pmatrix} 2 & 0 \\ 0 & 3 \end{pmatrix},
   \begin{pmatrix} 3 & 1 \\ 0 & 2 \end{pmatrix},
   \begin{pmatrix} 2 & 0 \\ 1 & 3 \end{pmatrix}  $$
So the span of matrices $A$ similar to $D$ is all of (real) $2\times 2$ matrices.
