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Year 2021, Volume: 25 Issue: 2, 610 - 618, 15.04.2021

Mutlu Akar

https://doi.org/10.16984/saufenbilder.869402
Cited By: 2

Abstract

References

  • [1] Akar, M., Sirakov, N. M. (2019), Support vector machine skin lesion classification in Clifford algebra subspaces, Applications of Mathematics, 64(5), 581-598.
  • [2] Brackx, F., De Schepper, N. ve Sommen F. (2006), Clifford-Hermite and two-dimensional Clifford-Gabor filters for early vision, 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering K. Gürlebeck and C. Könke (eds.) Weimar, Germany, 12-14 July.
  • [3] Lounesto, P. (2001), Clifford Algebras and Spinors, 2nd edition, Cambridge University Press.
  • [4] Aragon, J.L., Aragon-Camarasa, G., Aragon-Gonzalez, G. ve Rodriguez-Andrade, M.A. (2018), Clifford algebra with mathematica, arXiv:0810.2412v2 [math-ph] 22 January.
  • [5] Roy, S., Mitra, A. ve Setua, S. K. (2014), Color image representation using multivector, 2014 Fifth International Conference on Intelligent Systems, Modelling and Simulation, Langkawi, Malaysia, 27-29 January 2014, IEEE Xplore.
  • [6] Bayro-Corrochano, E. J. ve Arana-Daniel, N. (2010), Clifford support vector machines for classification, regression, and recurrence, IEEE Transactions on Neural Networks, 21(11), 1731-1746.
  • [7] Franchini, S., Vassallo, G. ve Sorbello, F. (2010), A brief introduction to Clifford algebra, University of Palermo, Department of Computer Engineering, Technical Report N. 2/2010.
  • [8] Vaz, J., Jr. ve Da Rocha, R., Jr., (2016), An introduction to Clifford algebras and spinors, Oxford University Press.
  • [9] Hitzer, E., Nitta , T. ve Kuroe, Y. (2013), Applications of Clifford’s geometric algebra, arXiv:1305.5663v1 [math.RA] 24 May.

The Essentials of Clifford Algebras with Maple Programming

Year 2021, Volume: 25 Issue: 2, 610 - 618, 15.04.2021

Mutlu Akar

https://doi.org/10.16984/saufenbilder.869402
Cited By: 2

Abstract

Clifford algebra (geometric algebra) which has many applications in physics, robotics, CAD (Computer-Aided Design) /CAM (Computer-Aided Manufacture), computer graphics, image processing, etc. is one of the important subjects in mathematics. In this paper, after we give the definition of Clifford algebras, introduce their subspaces. Firstly, we develop an algorithm which obtain some concepts of Clifford algebras using by Maple programming. Secondly, another algorithm calculates the norm of the multivector obtained by finding the Clifford product of any two vectors of the same finite dimension.

Keywords

Clifford algebras Clifford product Multivector Maple

References

  • [1] Akar, M., Sirakov, N. M. (2019), Support vector machine skin lesion classification in Clifford algebra subspaces, Applications of Mathematics, 64(5), 581-598.
  • [2] Brackx, F., De Schepper, N. ve Sommen F. (2006), Clifford-Hermite and two-dimensional Clifford-Gabor filters for early vision, 17th International Conference on the Application of Computer Science and Mathematics in Architecture and Civil Engineering K. Gürlebeck and C. Könke (eds.) Weimar, Germany, 12-14 July.
  • [3] Lounesto, P. (2001), Clifford Algebras and Spinors, 2nd edition, Cambridge University Press.
  • [4] Aragon, J.L., Aragon-Camarasa, G., Aragon-Gonzalez, G. ve Rodriguez-Andrade, M.A. (2018), Clifford algebra with mathematica, arXiv:0810.2412v2 [math-ph] 22 January.
  • [5] Roy, S., Mitra, A. ve Setua, S. K. (2014), Color image representation using multivector, 2014 Fifth International Conference on Intelligent Systems, Modelling and Simulation, Langkawi, Malaysia, 27-29 January 2014, IEEE Xplore.
  • [6] Bayro-Corrochano, E. J. ve Arana-Daniel, N. (2010), Clifford support vector machines for classification, regression, and recurrence, IEEE Transactions on Neural Networks, 21(11), 1731-1746.
  • [7] Franchini, S., Vassallo, G. ve Sorbello, F. (2010), A brief introduction to Clifford algebra, University of Palermo, Department of Computer Engineering, Technical Report N. 2/2010.
  • [8] Vaz, J., Jr. ve Da Rocha, R., Jr., (2016), An introduction to Clifford algebras and spinors, Oxford University Press.
  • [9] Hitzer, E., Nitta , T. ve Kuroe, Y. (2013), Applications of Clifford’s geometric algebra, arXiv:1305.5663v1 [math.RA] 24 May.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Mutlu Akar 0000-0003-3718-7449

Publication Date April 15, 2021
Submission Date January 27, 2021
Acceptance Date March 31, 2021
Published in Issue Year 2021 Volume: 25 Issue: 2

Cite

APA Akar, M. (2021). The Essentials of Clifford Algebras with Maple Programming. Sakarya University Journal of Science, 25(2), 610-618. https://doi.org/10.16984/saufenbilder.869402
AMA Akar M. The Essentials of Clifford Algebras with Maple Programming. SAUJS. April 2021;25(2):610-618. doi:10.16984/saufenbilder.869402
Chicago Akar, Mutlu. “The Essentials of Clifford Algebras With Maple Programming”. Sakarya University Journal of Science 25, no. 2 (April 2021): 610-18. https://doi.org/10.16984/saufenbilder.869402.
EndNote Akar M (April 1, 2021) The Essentials of Clifford Algebras with Maple Programming. Sakarya University Journal of Science 25 2 610–618.
IEEE M. Akar, “The Essentials of Clifford Algebras with Maple Programming”, SAUJS, vol. 25, no. 2, pp. 610–618, 2021, doi: 10.16984/saufenbilder.869402.
ISNAD Akar, Mutlu. “The Essentials of Clifford Algebras With Maple Programming”. Sakarya University Journal of Science 25/2 (April 2021), 610-618. https://doi.org/10.16984/saufenbilder.869402.
JAMA Akar M. The Essentials of Clifford Algebras with Maple Programming. SAUJS. 2021;25:610–618.
MLA Akar, Mutlu. “The Essentials of Clifford Algebras With Maple Programming”. Sakarya University Journal of Science, vol. 25, no. 2, 2021, pp. 610-8, doi:10.16984/saufenbilder.869402.
Vancouver Akar M. The Essentials of Clifford Algebras with Maple Programming. SAUJS. 2021;25(2):610-8.

Cited By

A generalization of Euler's formula in Clifford algebras
Mathematical Methods in the Applied Sciences
https://doi.org/10.1002/mma.8213
Current survey of Clifford geometric algebra applications
Mathematical Methods in the Applied Sciences
https://doi.org/10.1002/mma.8316
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