Given the linear transformation $\mathbb{R}^2 \rightarrow \mathbb{R}^2$ with:
$T:\begin{bmatrix} 1 \\ 0 \end{bmatrix}\mapsto\begin{bmatrix} 0 \\ 1 \end{bmatrix}$
and $T:\begin{bmatrix} 0 \\ 1 \end{bmatrix}\mapsto\begin{bmatrix} -1 \\ 0 \end{bmatrix}$
Provided that this transformation corresponds to the rotation clockwise by 90 degrees. (It sends $(x,y)$ to $(-y,x)$). Describe geometrically what the linear transformation S does.
I'm just confused what to add to the geometric description since it was provided that it was a rotation counterclockwise by 90 degrees. It sounds to me very similar to a rotation about the origin from geometry?
Best Answer
Yes, if you consider a general point $(a,b)$ then $T(a,b)=(-b,a)$. This means that the only fixed point is the origin. So the geometric interpretation as you said is a rotation of 90 degrees with center in the origin.