English

Quadratic forms and the expansion and rotations of linear endomorphisms

Rings and Algebras 2023-07-17 v1 Differential Geometry

Abstract

New expansionary and rotational quadratic forms are constructed for EnE^n-endomorphisms. Relations amongst the various eigenvalues, eigendirections and matrix invariants are established, including propositions on complexity and geometric multiplicity. The underlying construction involves a novel, almost-orthogonal expansion based on two-plane rotations. The development is strongly geometric in flavour and has application to the theory of connections, of which the Frenet case on E3E^3 is given as a model.

Keywords

Cite

@article{arxiv.2307.07132,
  title  = {Quadratic forms and the expansion and rotations of linear endomorphisms},
  author = {Geoff Prince},
  journal= {arXiv preprint arXiv:2307.07132},
  year   = {2023}
}