Jan 22, 2025
\[\begin{bmatrix} 1 & 0 \\ 0 & 0 \end{bmatrix}\]
.\[P_u = u u^T\]
.w = [2, 1, -2]
, first normalize w
to u
and then compute P_u
.\[\begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix}\]
.cos(θ), sin(θ)
-sin(θ), cos(θ)
[1, 3]
by 45 degrees using the rotation matrix for θ = π/4
.