Let $\bold{w} = \begin{pmatrix} 2 \ -1 \end{pmatrix}$. There exists a $2 imes 2$ matrix $\bold{P}$ such that

Question

Let $\bold{w} = \begin{pmatrix} 2 \ -1 \end{pmatrix}$. There exists a $2 \times 2$ matrix $\bold{P}$ such that
$$\text{proj}_{\bold{w}} \bold{v} = \bold{P} \bold{v}$$
for all 2-dimensional vectors $\bold{v}$. Find $\bold{P}$.

Steve · Answer

can you skip the LaTex? It appears that you are saying that w = (2,1) and there is a 2x2 P such that w•v = Pv or something like that. Correct?

Let $\bold{w} = \begin{pmatrix} 2 \\ -1 \end{pmatrix}$. There exists a $2 \times 2$ matrix $\bold{P}$ such that