On Fremdervectors: Vectors Orthogonal to Their Images Under Linear Transformations

Matthew G. Reuter

On Fremdervectors: Vectors Orthogonal to Their Images Under Linear Transformations

Rings and Algebras 2017-08-21 v2

Authors: Matthew G. Reuter

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.

Keywords

fremdervector eigenvector linear transformation orthogonal vector fremdervector value

Cite

@article{arxiv.1708.04141,
  title  = {On Fremdervectors: Vectors Orthogonal to Their Images Under Linear Transformations},
  author = {Matthew G. Reuter},
  journal= {arXiv preprint arXiv:1708.04141},
  year   = {2017}
}

Comments

6 pages, 0 figures

On Fremdervectors: Vectors Orthogonal to Their Images Under Linear Transformations

Abstract

Keywords

Cite

Comments

Related papers