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| geometric_algebra [2023/11/23 13:29] – [Videos] pbk | geometric_algebra [2024/10/11 17:06] (current) – [Videos] pbk |
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| * [[https://github.com/topics/geometric-algebra|Geometric Algebra]] topic at GitHub | * [[https://github.com/topics/geometric-algebra|Geometric Algebra]] topic at GitHub |
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| | * [[https://www.linkedin.com/groups/8278281|Pre-University Geometric Algebra]] LinkedIn group |
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| ==== General ==== | ==== General ==== |
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| > The last "Mathematische Annalen" contains a paper by H. Grassmann, on the application of his calculus of extension to Mechanics. He adopts the quaternion addition of vectors. But he has two multiplications, internal and external, just as the principles of logic require. (...) The relation of the two multiplications is exceedingly interesting. The system seems to me more suitable to three dimensional space, and also more natural than that of quaternions. The simplification of mechanical formulas is striking, but not more than quaternions would effect, that I see. | > The last "Mathematische Annalen" contains a paper by H. Grassmann, on the application of his calculus of extension to Mechanics. He adopts the quaternion addition of vectors. But he has two multiplications, internal and external, just as the principles of logic require. (...) The relation of the two multiplications is exceedingly interesting. The system seems to me more suitable to three dimensional space, and also more natural than that of quaternions. The simplification of mechanical formulas is striking, but not more than quaternions would effect, that I see. |
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| | * [[https://github.com/Dicklesworthstone/grassmann_article|The Lessons of Hermann Grassmann and the Nature of Abstractions]] - //Jeffrey Emanuel// |
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| | > (...) To cut the story short, these ideas were totally revolutionary, and he ended up collecting them all several years later in his groundbreaking work, Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik, published in 1844 when he was 35. Grassmann essentially came up with a totally original and new conception of linear algebra. Instead of the more traditional development of systems of linear equations, vectors, matrices, determinants, etc., Grassmann had a more general and abstract conception of the subject, which focused on what is now known as an exterior algebra, also known as the "wedge product." |
| ===== Lecture notes and tutorials ===== | ===== Lecture notes and tutorials ===== |
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| * [[https://www.youtube.com/playlist?list=PLsSPBzvBkYjxrsTOr0KLDilkZaw7UE2Vc|Plane-based Geometric Algebra Tutorial]] - Presentation at SIBGRAPI 2021, //Steven De Keninck and Leo Dorst//. | * [[https://www.youtube.com/playlist?list=PLsSPBzvBkYjxrsTOr0KLDilkZaw7UE2Vc|Plane-based Geometric Algebra Tutorial]] - Presentation at SIBGRAPI 2021, //Steven De Keninck and Leo Dorst//. |
| * [[https://www.youtube.com/watch?v=hTa_gErsrtM|Geometric Algebra]] - Talk at SIGGRAPH 2022, //Alyn Rockwood and Dietmar Hildenbrand//. | * [[https://www.youtube.com/watch?v=hTa_gErsrtM|Geometric Algebra]] - Talk at SIGGRAPH 2022, //Alyn Rockwood and Dietmar Hildenbrand//. |
| | * [[https://www.youtube.com/watch?v=8n6GsKWznfY|Plane Based Geometric Algebra]] - Advanced Computational Applications of GA, //Leo Dorst and Steven De Keninck//. |
| | * [[https://www.youtube.com/watch?v=PGZNYGwsXTw|Why Geometric Algebra Should be in the Standard Linear Algebra Curriculum]] and [[https://www.youtube.com/watch?v=ISKJPmuZkbY|Fun Applications of Geometric Algebra]] - Presentations at [[https://pgadey.ca/seminar/|Parker Glynn-Adey seminars]], //Logan Lim//. |
| * [[https://www.youtube.com/watch?v=VXziLgMIWf8|Geometric Clifford Algebra Networks and Clifford Neural Layers for PDE Modeling]] - Valence Labs, //Johannes Brandstetter//. | * [[https://www.youtube.com/watch?v=VXziLgMIWf8|Geometric Clifford Algebra Networks and Clifford Neural Layers for PDE Modeling]] - Valence Labs, //Johannes Brandstetter//. |
| * [[https://www.youtube.com/watch?v=nktgFWLy32U|Spinors for Beginners 11: What is a Clifford Algebra?]] - //eigenchris//. | * [[https://www.youtube.com/watch?v=nktgFWLy32U|Spinors for Beginners 11: What is a Clifford Algebra?]] - //eigenchris//. |
| * [[https://www.youtube.com/watch?v=1AmeD0Vc8ow|GAME2023 Geometric Algebra Mini Event]] - Livestream. | * [[https://www.youtube.com/watch?v=1AmeD0Vc8ow|GAME2023 Geometric Algebra Mini Event]] - Livestream. |
| * [[https://www.youtube.com/watch?v=zgi-13F2Kec|Geometric Algebra: The Prequel]] - at GAME2023, //Steven De Keninck//. | * [[https://www.youtube.com/watch?v=zgi-13F2Kec|Geometric Algebra: The Prequel]] - at GAME2023, //Steven De Keninck//. |
| | * [[https://www.youtube.com/watch?v=nPIRL-c88_E|Geometric Algebra Transformers: Revolutionizing Geometric Data]] - at Intelligent Systems Conference 2023, //Taco Cohen//. |
| | * [[https://www.youtube.com/@pre-universitygeometricalg5862|Pre-University Geometric Algebra Videos]] - This channel supports the [[https://www.linkedin.com/groups/8278281/|LinkedIn group]]. |
| | * [[https://www.youtube.com/watch?v=B035yDsLfDc&list=PL4TOpi2EWY8Z-FHbbosrBeTt66zQAupqx|Kind of an Intro to Geometric Algebra]] - //[[https://www.youtube.com/@EccentricTuber|Eccentric]]//. |
| | * [[https://www.youtube.com/watch?v=_THrv564rFA|Different approaches/notation for Projective Geometric Algebra from Eric Lengyel and Jon Selig]] - //Hamish Todd//. |
| | * [[https://www.youtube.com/watch?v=5RHSS-zMaAQ|The shocking connection between complex numbers and geometry]] - //Aleph 0//. |
| | * [[https://www.youtube.com/watch?v=jn98jLS87Sk&list=PLR1q-0FLgb_26n63bezVwGqIn1EwBjfvS|Clifford Algebra and the Standard Model]] - //Jason Blood//. |
| | * [[https://www.youtube.com/watch?v=KpS2GLBOyXU|Getting started with projective geometric algebra (PGA)]] - //UV Wizard//. |
| | * [[https://www.youtube.com/watch?v=xGuN6KM_D18|Amazing Things You Can Do in Geometric Algebra - Explained]] - //ThoughtThrill//. |
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| ===== Computing frameworks ===== | ===== Computing frameworks ===== |
| * [[https://github.com/markisus/g3|G3]] - A library for the Geometric Algebra of the Vector Space R^3, //Markisus//. | * [[https://github.com/markisus/g3|G3]] - A library for the Geometric Algebra of the Vector Space R^3, //Markisus//. |
| * [[https://github.com/vincentnozick/garamon|Garamon Generator]] - Geometric Algebra Recursive and Adaptative Monster is a generator of C++ libraries dedicated to Geometric Algebra, //Vincent Nozick, Stephane Breuils//. | * [[https://github.com/vincentnozick/garamon|Garamon Generator]] - Geometric Algebra Recursive and Adaptative Monster is a generator of C++ libraries dedicated to Geometric Algebra, //Vincent Nozick, Stephane Breuils//. |
| | * [[https://coreality.cc/clifford|Clifford Algebra Explorer]] - A powerful interactive tool for exploring the structures and properties of Clifford Algebras, //[[https://www.youtube.com/@OurCoreality|OurCoreality]]//. |
| ===== Articles ===== | ===== Articles ===== |
| * [[http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf|Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics]] (2002) - //David Hestenes// | * [[http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf|Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics]] (2002) - //David Hestenes// |
