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Geometric Neural Networks for Object Recognition
Published in Nancy Arana Daniel, Alma Y. Alanis, Carlos Lopez Franco, Neural Networks for Robotics: An Engineering Perspective, 2019
Nancy Arana Daniel, Alma Y. Alanis, Carlos Lopez Franco
Geometric Algebra also known as Clifford Algebra (CA), in fact represents a family of algebras that depend on a chosen vector space and on a special kind of product (the geometric product). The GA is a mathematical framework where we can find embedded concepts from linear algebra, tensor algebra, quaternion algebra, complex numbers and others. We represent a geometric algebra with Gp,q,r $ G_{p,q,r} $ 1.
Introduction
Published in Dietmar Hildenbrand, Introduction to Geometric Algebra Computing, 2020
Geometric Algebra is based on the work of the German high school teacher Hermann Grassmann and his vision of a general mathematical language for geometry. His very fundamental work, called Ausdehnungslehre [14], was little noted in his time. Today, however, Grassmann is more and more respected as one of the most important mathematicians of the 19th century. William Clifford [5] combined Grassmann’s exterior algebra and Hamilton’s quaternions in what we call Clifford algebra or Geometric Algebra1.
Dirichlet-type problems for n-Poisson equation in Clifford analysis
Published in Applicable Analysis, 2022
Clifford algebra is a number system generalizing the complex numbers, quaternions and hypercomplex number systems and defining the structure of the multi-dimensional universe. Clifford analysis is the function theory constructed based on Clifford algebra and it is introduced as a generalization of complex function theory to the higher dimensions with applications in science and engineering. Some basic results on Clifford analysis are presented in the Ph.D. thesis of G.N. Hile where the theory of generalized hyperanalytic functions, which is introduced by R.P. Gilbert, was studied, see [1–3]. The theory of Clifford analysis was developed by Delanghe, Brackx, Sommen [4] and has been studied by many authors, see [5–10] and references therein.