I am given the matrix $$ \begin{bmatrix} -1/2 & \sqrt{3}/2 \\ -\sqrt{3}/2 & -1/2\\ \end{bmatrix} $$
I think this is a reflection because I tied sketching a rough graph. However, I'm not sure how to find the line of reflection?
2026-03-26 14:20:35.1774534835
Determine whether the given the orthogonal matrix represents a roation or reflextion...?
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As $det(A)=1$, it is a rotation. Reflexion changes orientation, which would yield $det(A)=-1$. (This argument is valid only in the 2d-case.)
To find out the angle of rotation, compute the angle between $e_1$ and $Ae_1$.
If $A$ would be a reflection, the line of reflection is given by the eigenvector to the eigenvalue $1$.