What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
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
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
After our introduction to matrices and vectors and our first deeper dive into matrices, it is time for us to start the deeper dive into vectors. Vector spaces can be vectors, matrices, and even function. In this video I talk about vector spaces, subspaces, and the porperties of vector sp
From playlist Introducing linear algebra
Introduction to Vector Fields This video discusses, 1) The definition of a vector field. 2) Examples of vector fields including the gradient, and various velocity fields. 3) The definition of a conservative vector field. 4) The definition of a potential function. 5) Test for conservative
From playlist Calculus 3
Vector spaces | Lecture 16 | Matrix Algebra for Engineers
Definition of a vector space. Join me on Coursera: https://www.coursera.org/learn/matrix-algebra-engineers Lecture notes at http://www.math.ust.hk/~machas/matrix-algebra-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1
From playlist Matrix Algebra for Engineers
Definition of linear map. Algebraic properties of linear maps.
From playlist Linear Algebra Done Right
QED Prerequisites Geometric Algebra 8 Better notation for basis vectors
After some errata, we proceed into section 3.3 of our topic paper. This section cleans up our currently cumbersome notation of the spacetime algebra and provides a tight way to write down basis vectors. This notation also anticipates some important dualities that we will learn about soon.
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 6 - Multivector Products
This lesson begins by clearing up the definition of a "k-blade". Then we proceed to write down explicit expressions for most of the multivector products between vectors and bivectors, vectors and trivectors, and two bivectors. We do this using the "relative" formalism with a basis set give
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 5- Multivectors
In this lesson we introduce the idea of multivectors and emphasize the need to understand how to take the spacetime product of any two multivectors in the Spacetime Algebra. We demonstrate how this is done for the product between a vector and a bivector and we interpret the meaning of each
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 16: Canonical Bivectors
In this lesson we handle a few errata and then decompose a general bivector into a canonical form. Take note: we study this decomposition using a *different* paper, one written by Hestenes, but this is just a small diversion from our main paper. Please consider supporting this channel o
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 14: The Pseudoscalar
In this lesson we introduce the basis element of the grade 4 part of the spacetime algebra: the pseudoscalar. ERRATA: At about 6:00 I do a demonstration and slipped into the (-1,1,1,1) metric convention for a moment when I said (gamma_0)^2 = -1 …. An easy mistake to make! The result is st
From playlist QED- Prerequisite Topics
QED Prerequisites Geometric Algebra 10: Bivector-vector products
In this lesson we cover the spacetime product of a Bivector and a vector as presented in section 3.3.1 of our topic paper. Our topic paper can be found at: https://arxiv.org/abs/1411.5002 Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software
From playlist QED- Prerequisite Topics
Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum), Lecture 5
Quiver moduli spaces are algebraic varieties encoding the continuous parameters of linear algebra type classification problems. In recent years their topological and geometric properties have been explored, and applications to, among others, Donaldson-Thomas and Gromov-Witten theory have
From playlist Felix Klein Lectures 2020: Quiver moduli and applications, Markus Reineke (Bochum)
Geometry of vortices on Riemann surfaces (Lecture 3) by Oscar García-Prada
PROGRAM: VORTEX MODULI ORGANIZERS: Nuno Romão (University of Augsburg, Germany) and Sushmita Venugopalan (IMSc, India) DATE & TIME: 06 February 2023 to 17 February 2023 VENUE: Ramanujan Lecture Hall, ICTS Bengaluru For a long time, the vortex equations and their associated self-dual fie
From playlist Vortex Moduli - 2023
QED Prerequisites Geometric Algebra 9: Multivector Structure
This lesson continues with section 3.3 of the paper we are reviewing. That paper can be found here: https://arxiv.org/abs/1411.5002 Please consider supporting this channel on Patreon: https://www.patreon.com/XYLYXYLYX The software I usually use to produce the lectures is: https://app
From playlist QED- Prerequisite Topics
We have already looked at the column view of a matrix. In this video lecture I want to expand on this topic to show you that each matrix has a column space. If a matrix is part of a linear system then a linear combination of the columns creates a column space. The vector created by the
From playlist Introducing linear algebra
Markus Reineke - Cohomological Hall Algebras and Motivic Invariants for Quivers 4/4
We motivate, define and study Donaldson-Thomas invariants and Cohomological Hall algebras associated to quivers, relate them to the geometry of moduli spaces of quiver representations and (in special cases) to Gromov-Witten invariants, and discuss the algebraic structure of Cohomological H
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory