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
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
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
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
The formal definition of a vector space.
From playlist Linear Algebra Done Right
Multivariable Calculus | The notion of a vector and its length.
We define the notion of a vector as it relates to multivariable calculus and define its length. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
Vector Spaces andt Tensors | Wrap it Up!
In this video, I will summarize general vectorspaces on fields, bases, the dual vectorspace, and tensors/their components. This includes the dual basis definition. Translate This Video: Email : fematikaqna@gmail.com Discord: https://discord.gg/5z7pgj5 Subreddit : https://www.reddit.com/r/
From playlist Wrap It Up!
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
Lecture 18: Rotation and How to Represent It, Unit Quaternions, the Space of Rotations
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 In this lecture, Prof. Horn focuses on rotations, including its properties, repre
From playlist MIT 6.801 Machine Vision, Fall 2020
LieGroups and Lie Algebras: Lesson 4 - The Classical Groups Part II
Lie Groups and Lie Algebras: Lesson 4 - The Classical Groups Part II We introduce the idea of the classical matrix groups and their associated carrier spaces. In this video we discuss the representation of complex numbers and quaternions as matrices and then we discuss the idea of a metri
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 12 - The Classical Groups Part X (redux)
Lie Groups and Lie Algebras: Lesson 12 - The Classical Groups Part X (redux) We name the classical groups, finally! This video ended a bit short, I added the missing part in the "redux" version of this lesson. Please consider supporting this channel via Patreon: https://www.patreon.com/
From playlist Lie Groups and Lie Algebras
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
From playlist Unity game engine
Lie Groups and Lie Algebras: Lesson 3 - Classical Groups Part I
Lie Groups and Lie Algebras: Lesson 3 - Classical Groups Part I We introduce the idea of the classical matrix groups and their associated carrier spaces. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
Calculus 3: Vector Calculus in 2D (17 of 39) What is the Position Vector?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the position vector. The position vector indicates the position of a particle relative to the origin. The position usually depends on, or is a function of, a parametric variable (ex. t
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS
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
QED Prerequisites Geometric Algebra 24 Paravectors
In this lesson we discover yet another way to partition the components of a general multivector. In this method, the partitioning is entirely dependent on a choice of reference frame. That is \gamma_0 must be chosen and it represents the 4-velocity of an observer who is stationary in that
From playlist QED- Prerequisite Topics
A short video on terms such as Vector Space, SubSpace, Span, Basis, Dimension, Rank, NullSpace, Col space, Row Space, Range, Kernel,..
From playlist Tutorial 4