English

Self-Referential Definition of Orthogonality

General Mathematics 2009-04-03 v2

Abstract

There has for longer been an interest in finding equivalent conditions which define inner product spaces, and the respective literature is considerable, see for instance Amir, which lists 350 such results. Here, in this tradition, an alternative definition of orthogonality is presented which does not make use of any inner product. This definition, in the spirit of the recently developed non-wellfounded set theory, is self-referential, or circulatory.

Cite

@article{arxiv.0904.0082,
  title  = {Self-Referential Definition of Orthogonality},
  author = {Elemer E Rosinger and Gusti van Zyl},
  journal= {arXiv preprint arXiv:0904.0082},
  year   = {2009}
}
R2 v1 2026-06-21T12:46:56.407Z