Proof that the Kernel of a Linear Transformation is a Subspace
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Proof that the Kernel of a Linear Transformation is a Subspace
From playlist Proofs
What's a subspace of a vector space? How do we check if a subset is a subspace?
From playlist Linear Algebra
Linear Algebra: What is a Subspace?
Learn the basics of Linear Algebra with this series from the Worldwide Center of Mathematics. Find more math tutoring and lecture videos on our channel or at http://centerofmath.org/
From playlist Basics: Linear Algebra
A matrix of coefficients, when viewed in column form, is used to create a column space. This is simply the space created by a linear combination of the column vectors. A resulting vector, b, that does not lie in this space will not result in a solution to the linear system. A set of vec
From playlist Introducing linear algebra
Classic linear algebra exercise: the union of a subspace is a subspace if and only if one is contained in the other. This is also good practice with the definition of a subspace, and also shows how to prove statements of the form p implies (q or r) Check out my vector space playlist: http
From playlist Vector Spaces
Subspaces are the Natural Subsets of Linear Algebra | Definition + First Examples
A subspace is a subset that respects the two basic operations of linear algebra: vector addition and scalar multiplication. We say they are "closed under vector addition" and "closed under scalar multiplication". On a subspace, you can do linear algebra! Indeed, a subspace is an example of
From playlist Linear Algebra (Full Course)
Showing Nul(A) (the nullspace/kernel of A) is a subspace of Rn Check out my Matrix Algebra playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmAIZGo2l8SWvsHeeCLzamx0 Subscribe to my channel: https://www.youtube.com/channel/UCoOjTxz-u5zU0W38zMkQIFw
From playlist Linear Transformations
Cayley-Hamilton Theorem In this video, I state and prove one of the most important theorems in linear algebra: The Cayley-Hamilton Theorem. This theorem allows us to calculate some matrix equations from scratch, and intuitively says that A must satisfy its characteristic polynomial. This
From playlist Diagonalization
Vic Reiner, Lecture I - 9 February 2015
Vic Reiner (University of Minnesota) - Lecture I http://www.crm.sns.it/course/4036/ Many results in the combinatorics and invariant theory of reflection groups have q-analogues for the finite general linear groups GLn(Fq). These lectures will discuss several examples, and open questions a
From playlist Algebraic topology, geometric and combinatorial group theory - 2015
Galois theory: Primitive elements
This lecture is part of an online graduate course on Galois theory. We show that any finite separable extension of fields has a primitive element (or generator) and given n example of a finite non-separable extension with no primitive elements.
From playlist Galois theory
Representation theory: Abelian groups
This lecture discusses the complex representations of finite abelian groups. We show that any group is iomorphic to its dual (the group of 1-dimensional representations, and isomorphic to its double dual in a canonical way (Pontryagin duality). We check the orthogonality relations for the
From playlist Representation theory
Introduction to additive combinatorics lecture 9.5 --- Freiman's theorem for subsets of F_p^N.
Freiman's theorem for subsets of F_p^N states that if A is a subset of F_p^N and |A + A| is at most C|A|, then there is a subspace X of F_p^N of size at most C'|A| that contains A, where C' depends only on C. The result is actually due to Imre Ruzsa. Here I give not Ruzsa's original proof,
From playlist Introduction to Additive Combinatorics (Cambridge Part III course)
What is (a) Space? From Zero to Geo 1.5
What is space? In this video, we learn about the many different things that we might call "space". We come up with both a geometric and an algebraic definition, and the discussion also leads us to the important concept of subspaces. Sorry for how long this video took to make! I mention
From playlist From Zero to Geo
Motivic correlators and locally symmetric spaces - Alexander Goncharov
Locally Symmetric Spaces Seminar Topic: Motivic correlators and locally symmetric spaces Speaker: Alexander Goncharov Affiliation: Yale University; Member, School of Mathematics and Natural Sciences Date: October 3, 2017 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Roy Meshulam (6/27/17) Bedlewo: Concurrency Theory and Subspace Arrangements
Concurrency theory in computer systems deals with properties of systems in which several computations are executing simultaneously and potentially interacting with each other. We will be concerned with Dijkstra’s classical PV-model of concurrent computation. In this model, an execution cor
From playlist Applied Topology in Będlewo 2017
24. Structure of set addition IV: proof of Freiman's theorem
MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019 Instructor: Yufei Zhao View the complete course: https://ocw.mit.edu/18-217F19 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP62qauV_CpT1zKaGG_Vj5igX This lecture concludes the proof of Freiman's theorem on
From playlist MIT 18.217 Graph Theory and Additive Combinatorics, Fall 2019
Linear Algebra - Lecture 30 - Basis of a Subspace
In this video, I give the definition of "basis" for a subspace. Then, I work through the process for finding a basis for the null space and column space of any matrix.
From playlist Linear Algebra Lectures
Module Basics - Feb 17, 2021 - Rings and Modules
In this video we introduce basic notions like "cyclic" modules. This is the starting point for modules over PIDs.
From playlist Course on Rings and Modules (Abstract Algebra 4) [Graduate Course]