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arXiv · 2307.07132

Quadratic forms and the expansion and rotations of linear endomorphisms

Geoff Prince
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Abstract

New expansionary and rotational quadratic forms are constructed for $E^n$-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 $E^3$ is given as a model.

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Geoff Prince. 2023-07-14. Quadratic forms and the expansion and rotations of linear endomorphisms. https://arxiv.org/abs/2307.07132

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