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arXiv · 2309.13084

Global and Local Nilpotent Bases of Matrices

Garret Sobczyk
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Abstract

In studying the unusual properties of a special Witt basis of a Clifford geometric algebra with a Lorentz metric, a new concept of local duality makes it possible to define any real geometric algebra by complexifying this structure. Whereas a global basis of Witt null vectors is defined in terms of a pair of correlated Grassmann algebras in a geometric algebra of neutral signature, the special Witt basis of a Lorentz geometric algebra is defined in terms of a single Grassmann algebra. The relationship between these different concepts of duality, and their matrix representations, is studied in terms of simple examples. A surprising connection is exhibited between discrete Fourier and Wavelet transforms and the concept of local duality.

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Garret Sobczyk. 2023-09-21. Global and Local Nilpotent Bases of Matrices. https://arxiv.org/abs/2309.13084

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