Relevant bibliographies by topics / Clifford algebras

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Clifford algebras'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Clifford algebras"

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Aragón, G., J. L. Aragón, and M. A. Rodríguez. "Clifford algebras and geometric algebra." Advances in Applied Clifford Algebras 7, no. 2 (1997): 91–102. http://dx.doi.org/10.1007/bf03041220.

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Ceballos, Johan. "About the Dirichlet Boundary Value Problem using Clifford Algebras." JOURNAL OF ADVANCES IN MATHEMATICS 15 (November 12, 2018): 8098–119. http://dx.doi.org/10.24297/jam.v15i0.7795.

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This paper reviews and summarizes the relevant literature on Dirichlet problems for monogenic functions on classic Clifford Algebras and the Clifford algebras depending on parameters on. Furthermore, our aim is to explore the properties when extending the problem to and, illustrating it using the concept of fibres. To do so, we explore ways in which the Dirichlet problem can be written in matrix form, using the elements of a Clifford's base. We introduce an algorithm for finding explicit expressions for monogenic functions for Dirichlet problems using matrices in Finally, we illustrate how to
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DA ROCHA, ROLDÃO, ALEX E. BERNARDINI та JAYME VAZ. "κ-DEFORMED POINCARÉ ALGEBRAS AND QUANTUM CLIFFORD–HOPF ALGEBRAS". International Journal of Geometric Methods in Modern Physics 07, № 05 (2010): 821–36. http://dx.doi.org/10.1142/s0219887810004567.

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The Minkowski space–time quantum Clifford algebra structure associated with the conformal group and the Clifford–Hopf alternative κ-deformed quantum Poincaré algebra is investigated in the Atiyah–Bott–Shapiro mod 8 theorem context. The resulting algebra is equivalent to the deformed anti-de Sitter algebra [Formula: see text], when the associated Clifford–Hopf algebra is taken into account, together with the associated quantum Clifford algebra and a (not braided) deformation of the periodicity Atiyah–Bott–Shapiro theorem.
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Değırmencı, N., and Ş. Karapazar. "Explicit isomorphisms of real Clifford algebras." International Journal of Mathematics and Mathematical Sciences 2006 (2006): 1–13. http://dx.doi.org/10.1155/ijmms/2006/78613.

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It is well known that the Clifford algebraClp,qassociated to a nondegenerate quadratic form onℝn (n=p+q)is isomorphic to a matrix algebraK(m)or direct sumK(m)⊕K(m)of matrix algebras, whereK=ℝ,ℂ,ℍ. On the other hand, there are no explicit expressions for these isomorphisms in literature. In this work, we give a method for the explicit construction of these isomorphisms.
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Lewis, D. W. "A note on Clifford algebras and central division algebras with involution." Glasgow Mathematical Journal 26, no. 2 (1985): 171–76. http://dx.doi.org/10.1017/s0017089500005954.

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In this note we consider the question as to which central division algebras occur as the Clifford algebra of a quadratic form over a field. Non-commutative ones other than quaternion division algebras can occur and it is also the case that there are certain central division algebras D which, while not themselves occurring as a Clifford algebra, are such that some matrix ring over D does occur as a Clifford algebra. We also consider the further question as to which involutions on the division algebra can occur as one of two natural involutions on the Clifford algebra.
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Hasiewicz, Z., K. Thielemans, and W. Troost. "Superconformal algebras and Clifford algebras." Journal of Mathematical Physics 31, no. 3 (1990): 744–56. http://dx.doi.org/10.1063/1.528802.

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Kuznetsov, Sergey P., Vladimir V. Mochalov, and Vasiliy P. Chuev. "ALGORITHM FOR FINDING THE INVERSE ELEMENTS AND SOLUTION OF THE SILVESTER EQUATION IN THE CLIFFORD ALGEBRAS R4,0, R1,3, R5,0." Vestnik Chuvashskogo universiteta, no. 4 (December 26, 2023): 109–19. http://dx.doi.org/10.47026/1810-1909-2023-4-109-119.

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The purpose of the work is to find an algorithm for finding inverse elements in the Clifford algebras R4,0, R1,3, R5,0 and to solve the nonlinear Sylvester equation .
 
 Materials and methods. Using the basic conjugation operations in Clifford algebras, finding an algorithm for finding inverse elements. Application of this algorithm to solve the Sylvester equation.
 
 Results of the work. In Clifford algebras R4,0, R1,3, R5,0, which have a great application in physics, a method for finding inverse elements and equations for finding zero divisors were found. The found algori
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GLITIA, DANA DEBORA. "Modular G-graded algebras and G-algebras of endomorphisms." Carpathian Journal of Mathematics 30, no. 3 (2014): 301–8. http://dx.doi.org/10.37193/cjm.2014.03.14.

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We study Clifford Theory and field extensions for strongly group-graded algebras. In [Turull, A., Clifford theory and endoisomorphisms, J. Algebra 371 (2012), 510–520] and [Turull, A., Endoisomorphisms yield mo-dule and character correspondences, J. Algebra 394 (2013), 7–50] the author introduced the notion of endoisomorphism showing that there is a natural connection between it and Clifford Theory of finite group algebras. An endoisomorphism is an isomorphism between G-algebras of endomorphisms, where G is a finite group. We consider here endoisomorphisms between modules over strongly G-grade
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CASTRO, CARLOS. "POLYVECTOR SUPER-POINCARÉ ALGEBRAS, M, F THEORY ALGEBRAS AND GENERALIZED SUPERSYMMETRY IN CLIFFORD-SPACES." International Journal of Modern Physics A 21, no. 10 (2006): 2149–72. http://dx.doi.org/10.1142/s0217751x06028916.

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Starting with a review of the Extended Relativity Theory in Clifford-Spaces, and the physical motivation behind this novel theory, we provide the generalization of the nonrelativistic supersymmetric point-particle action in Clifford-space backgrounds. The relativistic supersymmetric Clifford particle action is constructed that is invariant under generalized supersymmetric transformations of the Clifford-space background's polyvector-valued coordinates. To finalize, the Polyvector super-Poincaré and M, F theory superalgebras, in D = 11, 12 dimensions, respectively, are discussed followed by our
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SCHOTT, RENÉ, and G. STACEY STAPLES. "OPERATOR CALCULUS AND INVERTIBLE CLIFFORD APPELL SYSTEMS: THEORY AND APPLICATION TO THE n-PARTICLE FERMION ALGEBRA." Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 01 (2013): 1350007. http://dx.doi.org/10.1142/s0219025713500070.

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Motivated by evolution equations on Clifford algebras and illustrated with the n-particle fermion algebra, a theory of invertible left- and right-Appell systems is developed for Clifford algebras of an arbitrary quadratic form. This work extends and clarifies the authors' earlier work on Clifford Appell systems, operator calculus, and operator homology/cohomology. A direct connection is also shown between blade factorization algorithms and the construction of Appell systems in these algebras.
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Dissertations / Theses on the topic "Clifford algebras"

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Han, Gang. "Clifford algebras associated with symmetric pairs /." View abstract or full-text, 2004. http://library.ust.hk/cgi/db/thesis.pl?MATH%202004%20HAN.

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Araujo, Martinho da Costa. "Construção de algebras reais de Clifford." reponame:Repositório Institucional da UFSC, 1988. http://repositorio.ufsc.br/xmlui/handle/123456789/75476.

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Dissertação (mestrado) - Universidade Federal de Santa Catarina. Centro de Ciencias Fisicas e Matematicas<br>Made available in DSpace on 2012-10-16T01:41:13Z (GMT). No. of bitstreams: 0Bitstream added on 2016-01-08T16:06:12Z : No. of bitstreams: 1 81779.pdf: 1134439 bytes, checksum: 3a7d46a6cf731cb8b57c4b1815f21112 (MD5)<br>O objetivo anunciado no título desta tese é realizado do seguinte modo: No capítulo I selecionamos definições de estruturas algébricas e de álgebra linear que usaremos nos capítulos posteriores. No capítulo II introduzimos a noção de álgebra de clifford. Estabelecemos a sua
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Wilmot, Gregory Paul. "The structure of Clifford algebra." Title page, contents and abstract only, 1988. http://web4.library.adelaide.edu.au/theses/09SM/09smw738.pdf.

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Hoefel, Eduardo Outeiral Correa. "Teorias de Gauge e algebras de Clifford." [s.n.], 2002. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307234.

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Orientador: Jayme Vaz Jr<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-02T06:58:26Z (GMT). No. of bitstreams: 1 Hoefel_EduardoOuteiralCorrea_M.pdf: 3091537 bytes, checksum: f00ee4b0eba7ea00e03a3ba084791085 (MD5) Previous issue date: 2002<br>Resumo: Nesta dissertação apresentamos uma descrição do formalismo matemático das teorias de gauge introduzindo os conceitos de grupos e álgebras de Lie, fibrados principais, conexões e curvatura. Em seguida introduzimos as álgebras de Clif
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Severi, Claudio. "Clifford algebras and spin groups, with physical applications." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18387/.

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In questo lavoro viene esposta la teoria delle algebre di Clifford e dei gruppi di Spin, con attenzione alle applicazioni fisiche, in particolare l'equazione di Dirac per particelle quantistiche con spin 1/2. I primi due capitoli sono dedicati ad una descrizione generale delle algebre di Clifford reali e complesse, che vengono costruite e classificate. Il terzo capitolo è dedicato ai gruppi di Spin ed alle loro algebre di Lie. Gli ultimi due capitoli illustrano un'applicazione fisica: viene esposta la teoria quantistica dello spin e del momento angolare, e si deriva l'equazione di Dirac con un
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Wylie, Dave. "Factoring Blades and Versors in Euclidean Clifford Algebras." Thesis, Southern Illinois University at Edwardsville, 2014. http://pqdtopen.proquest.com/#viewpdf?dispub=1564083.

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<p> This thesis examines different methods of factoring elements of Clifford Algebras, specifically, <i>C</i>&ell;<sub>n,0</sub>. Blades are factored using Fontijne's algorithm and other techniques. Versors are factored using Perwass's algorithm. Writing an element as a sum of blades, which are then factored, can make it more efficient to store or transmit that element. To evaluate the usefulness of expressing a given element of <i>C</i>&ell;<sub> n,0</sub> this way, the number of scalars required to express that element is compared between factored and expanded forms.</p>
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Buchholz, Sven [Verfasser]. "A Theory of Neural Computation with Clifford Algebras / Sven Buchholz." Kiel : Universitätsbibliothek Kiel, 2005. http://d-nb.info/1080317147/34.

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Doran, Christopher John Leslie. "Geometric algebra and its application to mathematical physics." Thesis, University of Cambridge, 1994. https://www.repository.cam.ac.uk/handle/1810/251691.

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Clifford algebras have been studied for many years and their algebraic properties are well known. In particular, all Clifford algebras have been classified as matrix algebras over one of the three division algebras. But Clifford Algebras are far more interesting than this classification suggests; they provide the algebraic basis for a unified language for physics and mathematics which offers many advantages over current techniques. This language is called geometric algebra - the name originally chosen by Clifford for his algebra - and this thesis is an investigation into the properties and app
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Resende, Adriana Souza. "Introdução elementar às álgebras Clifford 'CL IND.2' 'CL IND. 3'." [s.n.], 2010. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306698.

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Orientador: Waldyr Alves Rodrigues Junior<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matemática, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-15T23:09:32Z (GMT). No. of bitstreams: 1 Resende_AdrianaSouza_M.pdf: 17553204 bytes, checksum: a66cefe30e9957cc4351e03d3aec35b2 (MD5) Previous issue date: 2010<br>Resumo: O presente trabalho tem a intenção de apresentar por intermédio de uma linguagem unificada alguns conceitos de cálculo vetorial, álgebra linear (matrizes e transformações lineares) e também algumas idéias elem
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Rocha, Junior Roldão da. "Spinors e twistors no modelo paravetorial : uma formulação via algebras de Clifford." [s.n.], 2001. http://repositorio.unicamp.br/jspui/handle/REPOSIP/307233.

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Orientador: Jayme Vaz Junior<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-09-24T19:00:48Z (GMT). No. of bitstreams: 1 RochaJunior_Roldaoda_M.pdf: 4478856 bytes, checksum: 633cef106ddf91dc74b9d11ae74d1372 (MD5) Previous issue date: 2001<br>Resumo: Nesta dissertação o formalismo dos spinors e twistors de Penrose são formulados em termos das álgebras de Clifi'ord. Para tal utilizamos o modelo paravetorial do espaço-tempo, onde um vetor do espaço-tempo é escrito em termos da soma de
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Books on the topic "Clifford algebras"

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Kondrat'ev, Gennadiy. Clifford Geometric Algebra. INFRA-M Academic Publishing LLC., 2021. http://dx.doi.org/10.12737/1832489.

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The monograph is devoted to the fundamental aspects of geometric algebra and closely related issues. The category of Clifford algebras is considered as the conjugate category of vector spaces with a quadratic form. Possible constructions in this category and internal algebraic operations of an algebra with a geometric interpretation are studied. An application to the differential geometry of a Euclidean manifold based on a shape tensor is included.&#x0D; We consider products, coproducts and tensor products in the category of associative algebras with application to the decomposition of Cliffor
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Abłamowicz, Rafał, ed. Clifford Algebras. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2044-2.

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Klawitter, Daniel. Clifford Algebras. Springer Fachmedien Wiesbaden, 2015. http://dx.doi.org/10.1007/978-3-658-07618-4.

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Baylis, William E., ed. Clifford (Geometric) Algebras. Birkhäuser Boston, 1996. http://dx.doi.org/10.1007/978-1-4612-4104-1.

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Artibano, Micali, ed. Quadratic mappings and Clifford algebras. Birkhäuser, 2008.

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Lounesto, Pertti. Clifford algebras and spinors. Cambridge University Press, 1997.

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Perwass, Christian. Geometric algebra with applications in engineering. Springer, 2009.

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Meinrenken, Eckhard. Clifford Algebras and Lie Theory. Springer Berlin Heidelberg, 2013.

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Snygg, John. Clifford algebras: Computational toolfor physicists. Oxford University Press, 1997.

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Crumeyrolle, Albert. Orthogonal and Symplectic Clifford Algebras. Springer Netherlands, 1990. http://dx.doi.org/10.1007/978-94-015-7877-6.

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Book chapters on the topic "Clifford algebras"

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Eastwood, Michael. "Algebras Like Clifford Algebras." In Clifford Algebras. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2044-2_17.

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Scharlau, Winfried. "Clifford Algebras." In Grundlehren der mathematischen Wissenschaften. Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-642-69971-9_9.

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Husemoller, Dale. "Clifford Algebras." In Graduate Texts in Mathematics. Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4757-2261-1_12.

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Meinrenken, Eckhard. "Clifford algebras." In Clifford Algebras and Lie Theory. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36216-3_2.

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Cnops, Jan. "Clifford Algebras." In An Introduction to Dirac Operators on Manifolds. Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0065-9_1.

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Chevalley, Claude. "Clifford Algebras." In The Algebraic Theory of Spinors and Clifford Algebras. Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/978-3-642-60934-3_3.

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Lam, T. Y. "Clifford algebras." In Graduate Studies in Mathematics. American Mathematical Society, 2004. http://dx.doi.org/10.1090/gsm/067/05.

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Mitrea, Marius. "Clifford algebras." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/bfb0073557.

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Hassani, Sadri. "Clifford Algebras." In Mathematical Physics. Springer International Publishing, 2013. http://dx.doi.org/10.1007/978-3-319-01195-0_27.

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Hahn, Alexander J. "The Clifford Algebra in the Theory of Algebras, Quadratic Forms, and Classical Groups." In Clifford Algebras. Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-1-4612-2044-2_19.

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Conference papers on the topic "Clifford algebras"

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KRASNOV, YAKOV. "COMMUTATIVE ALGEBRAS IN CLIFFORD ANALYSIS." In Proceedings of the 3rd ISAAC Congress. World Scientific Publishing Company, 2003. http://dx.doi.org/10.1142/9789812794253_0041.

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Karmakar, Sanjay, and B. Rajan. "Multigroup-Decodable STBCs from Clifford Algebras." In 2006 IEEE Information Theory Workshop. IEEE, 2006. http://dx.doi.org/10.1109/itw.2006.322857.

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Karmakar, Sanjay, and B. Sundar Rajan. "Multigroup-Decodable STBCs from Clifford Algebras." In 2006 IEEE Information Theory Workshop. IEEE, 2006. http://dx.doi.org/10.1109/itw2.2006.323839.

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Chien, Steve, Lars Rasmussen, and Alistair Sinclair. "Clifford algebras and approximating the permanent." In the thiry-fourth annual ACM symposium. ACM Press, 2002. http://dx.doi.org/10.1145/509907.509944.

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Gürlebeck, Klaus, Wolfgang Sprössig, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "Analysis in Clifford Algebras—Some Aspects." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636713.

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Sprössig, Wolfgang, Klaus Gürlebeck, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Clifford Algebras in Mathematics and Applied Sciences." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790249.

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Furui, Sadataka. "Clifford algebras and physical and engineering sciences." In 11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013: ICNAAM 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4825542.

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Rajan, G. Susinder, and B. Sundar Rajan. "STBCs from Representation of Extended Clifford Algebras." In 2007 IEEE International Symposium on Information Theory. IEEE, 2007. http://dx.doi.org/10.1109/isit.2007.4557141.

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SCHOTT, RENÉ, and G. STACEY STAPLES. "CLIFFORD ALGEBRAS, RANDOM GRAPHS, AND QUANTUM RANDOM VARIABLES." In Quantum Stochastics and Information - Statistics, Filtering and Control. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812832962_0005.

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Ouyang, W., and Y. Wu. "Motion Representation and Inertial Navigation in Clifford Algebras." In 2022 DGON Inertial Sensors and Systems (ISS). IEEE, 2022. http://dx.doi.org/10.1109/iss55898.2022.9926412.

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