English

Two eigenvectors for the price of one

History and Overview 2021-06-28 v1

Abstract

Starting from a mistake done by a student, we discover an unexpected method of finding both eigenvectors for a 2×22\times2 matrix with distinct eigenvalues in a single computation. We discuss a connection with the Cayley-Hamilton theorem, and show the corresponding generalization for a 3×33 \times 3 matrix. The arguments should be understandable for strong linear algebra students.

Keywords

Cite

@article{arxiv.2106.13595,
  title  = {Two eigenvectors for the price of one},
  author = {Juan Tolosa},
  journal= {arXiv preprint arXiv:2106.13595},
  year   = {2021}
}

Comments

10 pages, no figures, multiple examples

R2 v1 2026-06-24T03:35:55.267Z