E.S.M. Hitzer

**Basic Multivector Calculus**

Proceedings of
*18th Intelligent Systems Symposium (FAN 2008)*,
23-24 Oct. 2008, Hiroshima, Japan, pp. 185 - 190 (2008).

**Abstract:**
We begin with introducing the generalization of real, complex, and quaternion numbers to hypercomplex
numbers, also known as Clifford numbers, or multivectors of geometric algebra. Multivectors encode everything from
vectors, rotations, scaling transformations, improper transformations (reflections, inversions), geometric objects (like
lines and spheres), spinors, and tensors, and the like. Multivector calculus allows to define functions mapping
multivectors to multivectors, differentiation, integration, function norms, multivector Fourier transformations and
wavelet transformations, filtering, windowing, etc. We give a basic introduction into this general mathematical
language, which has fascinating applications in physics, engineering, and computer science.

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[Geometric Calculus Japan index]