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
In this video, I show a very neat result about dual spaces: Namely, any basis of V* is automatically a dual basis of some basis of V. Even though this result is very interesting, it's the proof that makes this very exciting, by simply using the fact that V and V** are 'very' isomorphic. En
From playlist Dual Spaces
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
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
35 - Properties of bases (continued)
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
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)
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
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
Nonlinear algebra, Lecture 1: "Polynomials, Ideals, and Groebner Bases", by Bernd Sturmfels
This is the first lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences. Topics covered: polynomilas, ideals and Groebner bases.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Elisa Gorla: Complexity of Groebner bases computations and applications to cryptography - lecture 1
CIRM VIRTUAL EVENT Recorded during the meeting "French Computer Algebra Days" the March 02, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM's Audio
From playlist Virtual Conference
MAG - Lecture 7 - The Buchberger Criterion
metauni Algebraic Geometry (MAG) is a first course in algebraic geometry, in Roblox. In Lecture 7 we prove the Buchberger criterion, which allows us to recognise Grobner bases for ideals by looking at S-polynomials. The webpage for MAG is https://metauni.org/mag/. This video was recorded
From playlist MAG
Monica Vazirani: From representations of the rational Cherednik algebra to parabolic Hilbert schemes
Abstract: Young diagrams and standard tableaux on them parameterize irreducible representations of the symmetric group and their bases, respectively. There is a similar story for the double affine Hecke algebra (DAHA) taking periodic tableaux, or for the rational Cherednik algebra (a.k.a.
From playlist SMRI Algebra and Geometry Online
In this video, I show how to explicitly calculate dual bases. More specifically, I find the dual basis corresponding to the basis (2,1) and (3,1) of R^2. Hopefully this will give you a better idea of how dual bases work. Subscribe to my channel: https://www.youtube.com/c/drpeyam What is
From playlist Dual Spaces
P. Salberger - Quantitative aspects of rational points on algebraic varieties (part3)
Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour of N(B) when B goes to infinity. These conjectures can be studied using the Hardy-Littlewood m
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
MAG - Lecture 6 - The Hilbert Basis Theorem
metauni Algebraic Geometry (MAG) is a first course in algebraic geometry, in Roblox. In Lecture 6 we prove the Hilbert Basis Theorem, which says that in a polynomial ring over a field every ideal is finitely generated. The webpage for MAG is https://metauni.org/mag/. This video was recor
From playlist MAG
Tropical Geometry - Lecture 4 - Gröbner Bases and Tropical Bases | Bernd Sturmfels
Twelve lectures on Tropical Geometry by Bernd Sturmfels (Max Planck Institute for Mathematics in the Sciences | Leipzig, Germany) We recommend supplementing these lectures by reading the book "Introduction to Tropical Geometry" (Maclagan, Sturmfels - 2015 - American Mathematical Society)
From playlist Twelve Lectures on Tropical Geometry by Bernd Sturmfels
P. Salberger - Quantitative aspects of rational points on algebraic varieties (part2)
Let X be a subvariety of Pn defined over a number field and N(B) be the number of rational points of height at most B on X. There are then general conjectures of Manin on the asymptotic behaviour of N(B) when B goes to infinity. These conjectures can be studied using the Hardy-Littlewood m
From playlist Ecole d'été 2017 - Géométrie d'Arakelov et applications diophantiennes
Cluster characters, generic bases for cluster algebras (Lecture 4) by Pierre-Guy Plamondon
PROGRAM :SCHOOL ON CLUSTER ALGEBRAS ORGANIZERS :Ashish Gupta and Ashish K Srivastava DATE :08 December 2018 to 22 December 2018 VENUE :Madhava Lecture Hall, ICTS Bangalore In 2000, S. Fomin and A. Zelevinsky introduced Cluster Algebras as abstractions of a combinatoro-algebra
From playlist School on Cluster Algebras 2018
Linear Algebra - Lecture 31 - Coordinate Systems
In this video, I review the definition of basis, and discuss the notion of coordinates of a vector relative to that basis. The properties of a basis of a subspace guarantee that a vector in that subspace can be written as a linear combination of the basis vectors in only one way. The wei
From playlist Linear Algebra Lectures