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arXiv · 1708.04141

On Fremdervectors: Vectors Orthogonal to Their Images Under Linear Transformations

Matthew G. Reuter
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Abstract

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.

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Matthew G. Reuter. 2017-08-11. On Fremdervectors: Vectors Orthogonal to Their Images Under Linear Transformations. https://arxiv.org/abs/1708.04141

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