Dual basis definition and proof that it's a basis In this video, given a basis beta of a vector space V, I define the dual basis beta* of V*, and show that it's indeed a basis. We'll see many more applications of this concept later on, but this video already shows that it's straightforwar
From playlist Dual Spaces
Determine the Basis for a Set of Four Vectors in R3
This video explains how to determine the basis of a set of vectors in R3. https://mathispower4u.com
From playlist Linear Independence and Bases
Example of Rational Canonical Form 2: Several Blocks
Matrix Theory: Let A be a 12x12 real matrix with characteristic polynomial (x^2+1)^6, minimal polynomial (x^2 + 1)^3, and dim(Null(A^2 + I)) = 6. Find all possible rational canonical forms for A.
From playlist Matrix Theory
Example of Rational Canonical Form 3
Matrix Theory: We note two formulations of Rational Canonical Form. A recipe is given for combining and decomposing companion matrices using cyclic vectors.
From playlist Matrix Theory
Linear Algebra for Computer Scientists. 10. The Standard Basis
This computer science video is one of a series on linear algebra for computer scientists. In this video you will learn about the standard basis, otherwise known as the natural basis. The standard basis is an orthonormal set of vectors which can be used in linear combination to easily cre
From playlist Linear Algebra for Computer Scientists
Determine the Basis for a Set of Four Vectors in R3
This video explains how to determine the basis of a set of vectors in R3.
From playlist Linear Independence and Bases
Linear Algebra: Orthonormal Basis
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/ More on unit vectors: https://www.youtube.com/watch?v=C6EYJVBYXIo
From playlist Basics: Linear Algebra
Math 060 Fall 2017 111317C Orthonormal Bases
Motivation: how to obtain the coordinate vector with respect to a given basis? Definition: orthogonal set. Example. Orthogonal implies linearly independent. Orthonormal sets. Example of an orthonormal set. Definition: orthonormal basis. Properties of orthonormal bases. Example: Fou
From playlist Course 4: Linear Algebra (Fall 2017)
F[x]-Module Derivation of Rational and Jordan Canonical Forms
Similar matrices isomorphism proof: https://youtu.be/-ligAAxFM8Y Every module is a direct sum of cyclic modules: https://youtu.be/gWIRI43h0ic Intro to F[x]-modules: https://youtu.be/H44q_Urmts0 The rational canonical form and Jordan normal form of a matrix are very important tools in li
From playlist Ring & Module Theory
Tongmu He - Sen operators and Lie algebras arising from Galois representations over p-adic varieties
Any finite-dimensional p-adic representation of the absolute Galois group of a p-adic local field with imperfect residue field is characterized by its arithmetic and geometric Sen operators defined by Sen-Brinon. We generalize their construction to the fundamental group of a p-adic affine
From playlist Franco-Asian Summer School on Arithmetic Geometry (CIRM)
Tongmu He: Sen operators and Lie algebras arising from Galois representations over p-adic varieties
HYBRID EVENT Recorded during the meeting "Franco-Asian Summer School on Arithmetic Geometry in Luminy" the June 03, 2022 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Recanzone Find this video and other talks given by worldwide mathematicia
From playlist Algebraic and Complex Geometry
A tale of two bases - Anne Dranowski
Short Talks by Postdoctoral Members Topic: A tale of two bases Speaker: Anne Dranowski Affiliation: Member, School of Mathematics Date: September 23, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Linear Algebra 4.5 Coordinates and Basis
My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul
From playlist Linear Algebra
Example of Rational Canonical Form 1: Single Block
Matrix Theory: Let A be the real matrix [0 -1 1 0 \ 1 0 0 1 \ 0 0 0 -1 \ 0 0 1 0]. Find a matrix P that puts A into rational canonical form over the real numbers. We compare RCF with Jordan canonical form and review companion matrices. (Minor corrections added.)
From playlist Matrix Theory
[Lesson 1] QED Prerequisites Dirac Formalism Part I (redux)
(Editorial repair made in this version) This lecture is the first in a series of topics related to QED prerequisite material. I will be selecting some topics that students are often not clear about when arriving at QED. These topics cover a wide variety of material in elementary quantum m
From playlist QED- Prerequisite Topics
Overview of Jordan Canonical Form
Matrix Theory: We give an overview of the construction of Jordan canonical form for an nxn matrix A. The main step is the choice of basis that yields JCF. An example is given with two distinct eigenvalues.
From playlist Matrix Theory
