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| geometric_algebra [2021/10/20 08:03] – [Articles] pbk | geometric_algebra [2022/01/15 02:46] – [Lecture notes and tutorials] pbk |
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| * [[http://isites.harvard.edu/fs/docs/icb.topic1048774.files/clif_mein.pdf|Clifford algebras and Lie groups]] {{ga:clif_mein.pdf|(local)}}- //Eckhard Meinrenken//, University of Toronto. | * [[http://isites.harvard.edu/fs/docs/icb.topic1048774.files/clif_mein.pdf|Clifford algebras and Lie groups]] {{ga:clif_mein.pdf|(local)}}- //Eckhard Meinrenken//, University of Toronto. |
| * [[https://ocw.mit.edu/resources/res-8-001-applied-geometric-algebra-spring-2009|Applied Geometric Algebra]] (2009) - //László Tisza//, MIT OpenCourseWare. | * [[https://ocw.mit.edu/resources/res-8-001-applied-geometric-algebra-spring-2009|Applied Geometric Algebra]] (2009) - //László Tisza//, MIT OpenCourseWare. |
| | * [[https://www.cefns.nau.edu/~schulz/grassmann.pdf|Theory and application of Grassmann Algebra]] (2011) - //William C. Schulz//. |
| * [[https://lyseo.edu.ouka.fi/cms7/sites/default/files/geometric_algebra-tl.pdf|What is geometric algebra?]] (2016) - //Teuvo Laurinolli//, Oulun Lyseon. | * [[https://lyseo.edu.ouka.fi/cms7/sites/default/files/geometric_algebra-tl.pdf|What is geometric algebra?]] (2016) - //Teuvo Laurinolli//, Oulun Lyseon. |
| * [[https://www.zatlovac.eu/lecturenotes/GAIntroLagape.pdf|Geometric Algebra and Calculus: Unified Language for Mathematics and Physics]] (2018) - //Vaclav Zatloukal//, Czech Technical University in Prague. | * [[https://www.zatlovac.eu/lecturenotes/GAIntroLagape.pdf|Geometric Algebra and Calculus: Unified Language for Mathematics and Physics]] (2018) - //Vaclav Zatloukal//, Czech Technical University in Prague. |
| * [[https://dspace.library.uu.nl/bitstream/handle/1874/383367/IntroductionToGeometricAlgebraV2.pdf|Introduction to Geometric Algebra, a powerful tool for mathematics and physics]] (2019) - //Denis Lamaker//, Universiteit Utrecht. | * [[https://dspace.library.uu.nl/bitstream/handle/1874/383367/IntroductionToGeometricAlgebraV2.pdf|Introduction to Geometric Algebra, a powerful tool for mathematics and physics]] (2019) - //Denis Lamaker//, Universiteit Utrecht. |
| | * [[https://mattferraro.dev/posts/geometric-algebra|What is the Inverse of a Vector?]] (2021) - //Matt Ferraro//. |
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| ===== Videos ===== | ===== Videos ===== |
| * [[https://www.youtube.com/watch?v=tX4H_ctggYo|SIGGRAPH 2019: Geometric Algebra for Computer Graphics]] - //Charles Gunn// and //Steven De Keninck//. | * [[https://www.youtube.com/watch?v=tX4H_ctggYo|SIGGRAPH 2019: Geometric Algebra for Computer Graphics]] - //Charles Gunn// and //Steven De Keninck//. |
| * [[https://www.youtube.com/playlist?list=PLsSPBzvBkYjzcQ4eCVAntETNNVD2d5S79|GAME2020 - Geometric Algebra Mini Event]] - //DAE Kortrijk, Belgium//. | * [[https://www.youtube.com/playlist?list=PLsSPBzvBkYjzcQ4eCVAntETNNVD2d5S79|GAME2020 - Geometric Algebra Mini Event]] - //DAE Kortrijk, Belgium//. |
| * [[https://www.youtube.com/watch?v=60z_hpEAtD8|A Swift Introduction to Geometric Algebra]] - //sudgylacmoe//. | * [[https://www.youtube.com/watch?v=60z_hpEAtD8|A Swift Introduction to Geometric Algebra]] and [[https://www.youtube.com/playlist?list=PLVuwZXwFua-0Ks3rRS4tIkswgUmDLqqRy|From Zero to Geo]] - //sudgylacmoe//. |
| * [[https://www.youtube.com/watch?v=cKfC2ZBJulg|Projective Geometric Algebra for Paraxial Geometric Optics]] - // Katelyn Spadavecchia//. | * [[https://www.youtube.com/watch?v=cKfC2ZBJulg|Projective Geometric Algebra for Paraxial Geometric Optics]] - // Katelyn Spadavecchia//. |
| * [[https://www.youtube.com/watch?v=11sH9X0OO9Y&list=PLnpuwbuviU2j7OSnZdstP5_g1ejA32bYA|Geometric Algebra Lectures ]] - //Miroslav Josipović//. | * [[https://www.youtube.com/watch?v=11sH9X0OO9Y&list=PLnpuwbuviU2j7OSnZdstP5_g1ejA32bYA|Geometric Algebra Lectures ]] - //Miroslav Josipović//. |
| * [[https://dspace.library.uu.nl/bitstream/handle/1874/403340/thesis.pdf|Clifford algebras and their application in the Dirac equation]] (2021) - //Paul van Hoegaerden// | * [[https://dspace.library.uu.nl/bitstream/handle/1874/403340/thesis.pdf|Clifford algebras and their application in the Dirac equation]] (2021) - //Paul van Hoegaerden// |
| The aim of this thesis will be to study the Clifford algebras that appear in the derivation of the Dirac equation and investigate alternative formulations of the Dirac equation using (complex) quaternions. To this end, we will first look at the symmetries of the Dirac equation and some of the additional insights that follow from the Dirac equation. We will also give a derivation of the Dirac equation starting from the Schrödinger equation, in which we will come across the gamma matrices. | The aim of this thesis will be to study the Clifford algebras that appear in the derivation of the Dirac equation and investigate alternative formulations of the Dirac equation using (complex) quaternions. To this end, we will first look at the symmetries of the Dirac equation and some of the additional insights that follow from the Dirac equation. We will also give a derivation of the Dirac equation starting from the Schrödinger equation, in which we will come across the gamma matrices. |
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| | * [[https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/cta.3132|Geometric Algebra for teaching AC Circuit Theory]] (2021) - //Francisco G. Montoya, Raúl Baños et al// |
| | This paper presents and discusses the usage of Geometric Algebra (GA) for the analysis of electrical alternating current (AC) circuits. The potential benefits of this novel approach are highlighted in the study of linear and nonlinear circuits with sinusoidal and non-sinusoidal sources in the frequency domain, which are important issues in electrical engineering undergraduate courses. |
| ===== Books ===== | ===== Books ===== |
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