On Fremdervectors: Vectors Orthogonal to Their Images Under Linear Transformations
Abstract
Geometrically, the eigenvectors of a square matrix A are not rotated by A. Here we consider vectors that are rotated π/2 by A; that is, vectors orthogonal to their images. We call these vectors fremdervectors of A and discuss conditions for their existence. We also define fremdervalues, scalars z such that zI-A has a fremdervector, and discuss several known applications for fremdervectors.
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