Can you please explain this question to me?
Suppose that $w = [1,2,3]^T$ and $L: \mathbb{R}^3\to \mathbb{R}^3$ is defined by $L(x) =\text{Proj}_w(x)$ (projection of $x$ onto $w$). Compute the standard matrix of $[L]$ of the linear transformation.
Sorry for the format, i don't know how to use the website very well
Hint: L(x) is a linear transformation
I couldn't compute the projection because $x$ is missing. Thanks.
The matrix that projects onto the $1$-dimensional vector space spanned by $\mathrm{w}$, which is a line, is
$$\mathrm{P}_{\mathrm{w}} := \dfrac{\mathrm{w} \mathrm{w}^T}{\mathrm{w}^T \mathrm{w}} = \frac{1}{14} \begin{bmatrix} 1 & 2 & 3\\ 2 & 4 & 6\\ 3 & 6 & 9\end{bmatrix}$$