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
Astronomy - Ch. 27: Quasars (1 of 14) What Are Quasars?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn what is a quasar. A quasar (QUASi StellaR) is a very luminous object, initially discovered by the emission of powerful
From playlist ASTRONOMY 27 QUASARS
The Quaternion Symmetry Group – Vi Hart
From playlist G4G11 Videos
This is lecture 9 of an online mathematics course on groups theory. It covers the quaternions group and its realtion to the ring of quaternions.
From playlist Group theory
Particle Physics (13 of 41) Elementary Particles: What Is A Quark? (Part 1)
Visit http://ilectureonline.com for more math and science lectures! In this video I will give a detail description of quarks. Next video in the Particle Physics series can be seen at: https://youtu.be/De0U8fUBI7o
From playlist PHYSICS 65 PARTICLE PHYSICS
This week we learn what a QUASAR is! One of the most luminous objects in the Universe found shining brightly at the heart of distant galaxies. Quasars belong to a group of objects known as AGN, Active Galactic Nuclei. ----------------- As well as using information I already knew, I used a
From playlist PBSDS Galentines Day Playlist
Visualizing quaternions (4d numbers) with stereographic projection
How to think about this 4d number system in our 3d space. Part 2: https://youtu.be/zjMuIxRvygQ Interactive version of these visuals: https://eater.net/quaternions Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of t
From playlist Explainers
Abel Lecture — The future of mathematical physics: new ideas in old bottles — M. Atiyah — ICM2018
Mathematics and Physics have a rich and intricate history, going back at least to Pythagoras and Archimedes. In the last fifty years it has expanded in new directions but the future is uncertain. I propose to peer into the future using old ideas of Archimedes. We still have much to learn f
From playlist Special / Prizes Lectures
Improved torsion-point attacks on SIDH variants
Paper by Victoria de Quehen, Peter Kutas, Chris Leonardi, Chloe Martindale, Lorenz Panny, Christophe Petit, Katherine E. Stange presented at Crypto 2021 See https://iacr.org/cryptodb/data/paper.php?pubkey=31218. The conference program is at https://crypto.iacr.org/2021/program.php
From playlist My Collaborators
Lecture 19: Absolute Orientation in Closed Form, Outliers and Robustness, RANSAC
MIT 6.801 Machine Vision, Fall 2020 Instructor: Berthold Horn View the complete course: https://ocw.mit.edu/6-801F20 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP63pfpS1gV5P9tDxxL_e4W8O This lecture discusses photogrammetry topics and absolute orientation. We will al
From playlist MIT 6.801 Machine Vision, Fall 2020
Sir Michael Atiyah - From Algebraic Geometry to Physics - a Personal Perspective [2010]
Slides for this talk: https://drive.google.com/open?id=1JAtO2i5e-G3d4DuQ0OHuu_gkUCjLY7Rc Name: Michael Atiyah Event: Simons Center Building Inauguration Conference Title: From Algebraic Geometry to Physics - a Personal Perspective Date: 2010-11-10 @9:00 AM http://scgp.stonybrook.edu/vid
From playlist Mathematics
Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https://twitter.com/worldscienceu
From playlist Science Unplugged: Particle Physics
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
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
Set Theory (Part 14b): Quaternions and 3D Rotations
No background in sets needed for this video - learn about the foundations of quaternions, derivation of the Hamilton product, and their application to 3D rotations. We will also see how dot and cross products are related to quaternion math. This video will be of particular interest to comp
From playlist Set Theory by Mathoma
Computing Euler Angles: Tracking Attitude Using Quaternions
In this video we continue our discussion on how to track the attitude of a body in space using quaternions. The quaternion method is similar to the Euler Kinematical Equations and Poisson’s Kinematical Equations in that it consumes rate gyro information to compute Euler angles. However,
From playlist Flight Mechanics
Quaternions: Extracting the Dot and Cross Products
The most important operations upon vectors include the dot and cross products and are indispensable for doing physics and vector calculus. The dot product gives a quick way to check whether vectors are orthogonal and the cross product calculates a new vector orthogonal to both its inputs.
From playlist Quaternions
Astronomy - Ch. 27: Quasars (2 of 14) When Were Quasars First Discovered?
Visit http://ilectureonline.com for more math and science lectures! To donate: http://www.ilectureonline.com/donate https://www.patreon.com/user?u=3236071 We will learn that quasars were first discovered in the 1950's by astronomers using radio telescopes. When searching the sky they beg
From playlist ASTRONOMY 27 QUASARS
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