منابع مشابه
Clifford Algebra with Mathematica
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main ideas of Clifford algebra, with the main goal to develop a package for Clifford algebra calculations for the computer algebra program Mathematica∗. The Cliffor...
متن کاملClifford Algebra of the Vector Space of Conics for decision boundary Hyperplanes in m-Euclidean Space
In this paper we embed m-dimensional Euclidean space in the geometric algebra Clm to extend the operators of incidence in R to operators of incidence in the geometric algebra to generalize the notion of separator to a decision boundary hyperconic in the Clifford algebra of hyperconic sections denoted as Cl(V2). This allows us to extend the concept of a linear perceptron or the spherical percept...
متن کاملClifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space
A new method for constructing Clifford algebra-valued orthogonal polynomials in the open unit ball of Euclidean space is presented. In earlier research, we only dealt with scalar-valued weight functions. Now the class of weight functions involved is enlarged to encompass Clifford algebra-valued functions. The method consists in transforming the orthogonality relation on the open unit ball into ...
متن کاملClifford algebra as quantum language
We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using such representations for their permutations obey Clifford statistics. The vectors supporting the Clifford algebras of permutations and rotations are plexors an...
متن کاملClifford Type Algebra Characteristics Investigation
There are many applications of hypercomplex number systems in the methods of processing and presenting information. The quaternion system has particular importance, applications which can solve many practical problems: the navigation and management of mobile objects, in mechanics, electrodynamics, cryptography, digital signal processing, and others. Numerous applications of quaternions is cause...
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ژورنال
عنوان ژورنال: Advances in Applied Clifford Algebras
سال: 2001
ISSN: 0188-7009,1661-4909
DOI: 10.1007/bf03219144