  Geometrically, the eigenvectors of a square matrix $\mathbf{A}$ are not
rotated by $\mathbf{A}$. Here we consider vectors that are rotated $\pi/2$ by
$\mathbf{A}$; that is, vectors orthogonal to their images. We call these
vectors fremdervectors of $\mathbf{A}$ and discuss conditions for their
existence. We also define fremdervalues, scalars $z$ such that
$z\mathbf{I}-\mathbf{A}$ has a fremdervector, and discuss several known
applications for fremdervectors.
