Self-Referential Definition of Orthogonality

Elemer E Rosinger; Gusti van Zyl

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arXiv · 0904.0082

Self-Referential Definition of Orthogonality

Elemer E Rosinger·Gusti van Zyl

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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.

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Elemer E Rosinger, Gusti van Zyl. 2009-04-03. Self-Referential Definition of Orthogonality. https://arxiv.org/abs/0904.0082

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