Analytic geometry | Orientation (geometry) | Linear algebra
The orientation of a real vector space or simply orientation of a vector space is the arbitrary choice of which ordered bases are "positively" oriented and which are "negatively" oriented. In the three-dimensional Euclidean space, right-handed bases are typically declared to be positively oriented, but the choice is arbitrary, as they may also be assigned a negative orientation. A vector space with an orientation selected is called an oriented vector space, while one not having an orientation selected, is called unoriented. In mathematics, orientability is a broader notion that, in two dimensions, allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed. In linear algebra over the real numbers, the notion of orientation makes sense in arbitrary finite dimension, and is a kind of asymmetry that makes a reflection impossible to replicate by means of a simple displacement. Thus, in three dimensions, it is impossible to make the left hand of a human figure into the right hand of the figure by applying a displacement alone, but it is possible to do so by reflecting the figure in a mirror. As a result, in the three-dimensional Euclidean space, the two possible basis orientations are called right-handed and left-handed (or right-chiral and left-chiral). (Wikipedia).
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
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
This video explains how to sketch vectors in R^3, how to determine the magnitude of a vector and how to determine a unit vector. http://mathispower4u.yolasite.com/
From playlist Vectors
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
Calculus 3: Vector Calculus in 2D (19 of 39) Position Vector Example
Visit http://ilectureonline.com for more math and science lectures! In this video I will find the position vector=? along a circle of radius r(t) where t=angle of the position vector. Next video in the series can be seen at: https://youtu.be/x2LhfDnNDxs
From playlist CALCULUS 3 CH 3 VECTOR CALCULUS
13 Velocity and acceleration in 3D with cylindrical coordinates on the blackboard
In this video I show the derivation for velocity and acceleration in dimensional space, using cylindrical coordinates for the intermediate frame (body coordinate system)
From playlist Life Science Math: Vectors
The formal definition of a vector space.
From playlist Linear Algebra Done Right
Lecture 2 | Introduction to Robotics
Lecture by Professor Oussama Khatib for Introduction to Robotics (CS223A) in the Stanford Computer Science Department. Professor Khatib shows a video on Walking Machines then goes into his first topic -- Kinematics. CS223A is an introduction to robotics which covers topics such as Spati
From playlist Lecture Collection | Introduction to Robotics
Lecture 3: Exterior Algebra (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
What is a Tensor? Lesson 38: Visualization of Forms: Tacks and Sheaves. And Honeycombs.
What is a Tensor? Lesson 38: Visualization of Forms Part 2 Continuing to complete the "visualization" of the four different 3-dimensional vector spaces when dim(V)=3. Erratta: Note: When the coordinate system is expanded the density of things *gets numerically larger* and the area/volum
From playlist What is a Tensor?
AMMI Course "Geometric Deep Learning" - Lecture 10 (Gauges) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July-August 2021 by Michael Bronstein (Imperial College/Twitter), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 10: Gauges • Gauge transformat
From playlist AMMI Geometric Deep Learning Course - First Edition (2021)
Worldwide Calculus: Stokes' Theorem
Lecture on 'Stokes' Theorem' from 'Worldwide Multivariable Calculus'. For more lecture videos and $10 digital textbooks, visit www.centerofmath.org.
From playlist Integration and Vector Fields
Topological Analysis of Grain Boundaries - Srikanth Patala
Srikanth Patala Masachusetts Institute of Technology February 1, 2011 GEOMETRY AND CELL COMPLEXES Polycrystalline materials, such as metals, ceramics and geological materials, are aggregates of single-crystal grains that are held together by highly defective boundaries. The structure of g
From playlist Mathematics
Why do we care about vectors? From Zero To Geo 1.1
Why do we care about vectors? Vectors are an incredibly important concept both in geometric algebra and in modern mathematics in general. In this video, I show the motivation for the interpretation of vectors as arrows. After that, I describe the basics of this conception of vectors. T
From playlist From Zero to Geo
Definition of spherical coordinates | Lecture 33 | Vector Calculus for Engineers
We define the relationship between Cartesian coordinates and spherical coordinates; the position vector in spherical coordinates; the volume element in spherical coordinates; the unit vectors; and how to differentiate the spherical coordinate unit vectors. Join me on Coursera: https://www
From playlist Vector Calculus for Engineers
AMMI 2022 Course "Geometric Deep Learning" - Lecture 10 (Gauges) - Taco Cohen
Video recording of the course "Geometric Deep Learning" taught in the African Master in Machine Intelligence in July 2022 by Michael Bronstein (Oxford), Joan Bruna (NYU), Taco Cohen (Qualcomm), and Petar Veličković (DeepMind) Lecture 10: Gauges • Gauge transformations • Examples of gauge
From playlist AMMI Geometric Deep Learning Course - Second Edition (2022)
Index Theory, survey - Stephan Stolz [2018]
TaG survey series These are short series of lectures focusing on a topic in geometry and topology. May_8_2018 Stephan Stolz - Index Theory https://www3.nd.edu/~math/rtg/tag.html (audio fixed)
From playlist Mathematics
This is the second video of a series from the Worldwide Center of Mathematics explaining the basics of vectors. This video deals with vectors in the 2D and 3D planes, and shows the geometric interpretations of some vector operations. For more math videos, visit our channel or go to www.cen
From playlist Basics: Vectors
PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics
From playlist Dualities in Topology and Algebra (Online)