{"paper":{"title":"On Fremdervectors: Vectors Orthogonal to Their Images Under Linear Transformations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"Matthew G. Reuter","submitted_at":"2017-08-11T01:30:34Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.04141","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}