This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for
From playlist Quaternions
Quaternions as 4x4 Matrices - Connections to Linear Algebra
In math, it's usually possible to view an object or concept from many different (but equivalent) angles. In this video, we will see that the quaternions may be viewed as 4x4 real-valued matrices of a special form. What is interesting here is that if you know how to multiply matrices, you a
From playlist Quaternions
Matrix Theory: For the quaternion alpha = 1 - i + j - k, find the norm N(alpha) and alpha^{-1}. Then write alpha as a product of a length and a direction.
From playlist Matrix Theory
Geometric Algebra - Rotors and Quaternions
In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading
From playlist Math
The Quaternion Symmetry Group – Vi Hart
From playlist G4G11 Videos
Made from 24 heptagons. Source code and meshes here: https://github.com/timhutton/klein-quartic
From playlist Geometry
Set Theory (Part 14c): More on the Quaternions
No background in sets required for this video. In this video, we will learn how the quaternions can be thought of as pairings of complex numbers. We also will show how the quaternions can be written as a 2x2 complex matrix as opposed to a 4x4 real matrix and how the unit quaternions form t
From playlist Set Theory
Quaternion algebras via their Mat2x2(F) representations
In this video we talk about general quaternion algebras over a field, their most important properties and how to think about them. The exponential map into unitary groups are covered. I emphasize the Hamiltionion quaternions and motivate their relation to the complex numbers. I conclude wi
From playlist Algebra
Sonya Hanson - Pose estimation, temperature, noise, and biological temperature sensors via cryo-EM
Recorded 17 November 2022. Sonya Hanson of the Flatiron Institute presents "Better treatments of pose estimation, temperature, noise, and heterogeneity toward understanding biological temperature sensors via cryo-EM" at IPAM's Cryo-Electron Microscopy and Beyond Workshop. Abstract: With th
From playlist 2022 Cryo-Electron Microscopy and Beyond
The rotation problem and Hamilton's discovery of quaternions III | Famous Math Problems 13c
This is the third lecture on the problem of how to extend the algebraic structure of the complex numbers to deal with rotations in space, and Hamilton's discovery of quaternions, and here we roll up the sleaves and get to work laying out a concise but logically clear framework for this rem
From playlist Famous Math Problems
Lie Groups and Lie Algebras: Lesson 30 - SL(1,Q) from sl(1,Q)
Lie Groups and Lie Algebras: Lesson 30 - SL(1,Q) from sl(1,Q)' I this lecture we examine the lesser known member of the three Lie groups that share the "angular momentum" algebra: The Special Linear Group of transformations of a one dimensional quaternionic vector space. This is an exampl
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 2 - Quaternions
This video is about Lie Groups and Lie Algebras: Lesson 2 - Quaternions We study the algebraic nature of quaternions and cover the ideas of an algebra and a field. Later we will discover how quaternions fit into the description of the classical Lie Groups. NOTE: An astute viewer noted th
From playlist Lie Groups and Lie Algebras
Matching Paired Sets of Space and Orientation Data
To learn more about Wolfram Technology Conference, please visit: https://www.wolfram.com/events/technology-conference/ Speaker: Andrew Hanson Wolfram developers and colleagues discussed the latest in innovative technologies for cloud computing, interactive deployment, mobile devices, and
From playlist Wolfram Technology Conference 2018
Finding cocompact Fuchsian groups of given trace field and quaternian algebra - Jeremy Kahn
Jeremy Kahn, IAS October 7, 2015 http://www.math.ias.edu/wgso3m/agenda 2015-2016 Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academic year
From playlist Workshop on Geometric Structures on 3-Manifolds
G. Molino - The Horizontal Einstein Property for H-Type sub-Riemannian Manifolds
We generalize the notion of H-type sub-Riemannian manifolds introduced by Baudoin and Kim, and then introduce a notion of parallel Clifford structure related to a recent work of Moroianu and Semmelmann. On those structures, we prove an Einstein property for the horizontal distribution usin
From playlist Journées Sous-Riemanniennes 2018
Real and symmetric Springer theory - David Nadler
Virtual Workshop on Recent Developments in Geometric Representation Theory Topic: Real and symmetric Springer theory Speaker: David Nadler Affiliation: University of California, Berkeley Date: November 20, 2020 For more video please visit http://video.ias.edu
From playlist Virtual Workshop on Recent Developments in Geometric Representation Theory
Giuseppe De Nittis : Topological nature of the Fu-Kane-Mele invariants
Abstract: Condensed matter electronic systems endowed with odd time-reversal symmetry (TRS) (a.k.a. class AII topological insulators) show topologically protected phases which are described by an invariant known as Fu-Kane-Mele index. The construction of this in- variant, in its original f
From playlist Mathematical Physics
Mathematics in Post-Quantum Cryptography II - Kristin Lauter
2018 Program for Women and Mathematics Topic: Mathematics in Post-Quantum Cryptography II Speaker: Kristin Lauter Affiliation: Microsoft Research Date: May 22, 2018 For more videos, please visit http://video.ias.edu
From playlist My Collaborators
