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- W2119874683 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. th century mathematician H. Grassmann had the clear vision, that his extension theory (now developed to geometric calculus) … forms the keystone of the entire structure of mathematics.(6) The algebraic grammar of this universal form of calculus is geometric algebra (or Clifford algebra). That geometric calculus is a truly unifying approach to all of calculus will be demonstrated here by developing some basics of the vector differential calculus part of geometric calculus." @default.
- W2119874683 created "2016-06-24" @default.
- W2119874683 creator A5051974422 @default.
- W2119874683 date "2013-06-01" @default.
- W2119874683 modified "2023-09-26" @default.
- W2119874683 title "Basic Multivector Calculus" @default.
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