Find the matrix $\mathbf{P}$ such that for any vector $\mathbf{v},$ $\mathbf{P} \mathbf{v}$ is the projection of $\mathbf{v}$ onto the $y$-axis.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the matrix $\mathbf{P}$ such that for any vector $\mathbf{v},$ $\mathbf{P} \mathbf{v}$ is the projection of $\mathbf{v}$ onto the $y$-axis.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
\begin{pmatrix} 0 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{pmatrix}
Find the matrix $\mathbf{P}$ such that for any vector $\mathbf{v},$ $\mathbf{P} \mathbf{v}$ is the projection of $\mathbf{v}$ onto the $y$-axis.
train