Bilinear maps | Operations on vectors | Octonions
In mathematics, the seven-dimensional cross product is a bilinear operation on vectors in seven-dimensional Euclidean space. It assigns to any two vectors a, b in a vector a × b also in . Like the cross product in three dimensions, the seven-dimensional product is anticommutative and a × b is orthogonal both to a and to b. Unlike in three dimensions, it does not satisfy the Jacobi identity, and while the three-dimensional cross product is unique up to a sign, there are many seven-dimensional cross products. The seven-dimensional cross product has the same relationship to the octonions as the three-dimensional product does to the quaternions. The seven-dimensional cross product is one way of generalizing the cross product to other than three dimensions, and it is the only other bilinear product of two vectors that is vector-valued, orthogonal, and has the same magnitude as in the 3D case. In other dimensions there are vector-valued products of three or more vectors that satisfy these conditions, and binary products with bivector results. (Wikipedia).
Calculus 3: Vector Calculus in 3-D (18 of 35) What is a Cross Product?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a cross product. The cross product of 2 vectors A and B is another vector C and is directed perpendicular to the plane containing A and B. Next video in the series can be seen at: htt
From playlist THE "WHAT IS" PLAYLIST
Ex 2: Properties of Cross Products - Cross Product of a Sum and Difference
This video explains how to find the cross product of a sum and difference of two vectors. Site: http://mathispower4u.com
From playlist Vectors in Space (3D)
Unit Vector Perpendicular to Two Vectors
Multivariable Calculus: Find a unit vector perpendicular to the vectors u = (1,2,1) and v = (2,1,1). The main tool is the cross product.
From playlist Calculus Pt 7: Multivariable Calculus
Multivariable Calculus | The Cross Product
We define the cross product, give a few examples, and state a few properties. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
Ex 1: Properties of Cross Products - Cross Product of a Sum and Difference
This video explains how to find the cross product of a sum and difference of two vectors. Site: http://mathispower4u.com
From playlist Vectors in Space (3D)
Physics 1 - Vectors (16 of 21) Product Of Vectors: Cross Product: Vector Product
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the cross product, or vector product. Next video in this series can be seen at: https://youtu.be/hU7Qlu92GGE
From playlist Michel van Biezen: Physics Mechanics 1: Introduction, Standard Units, and Vectors
The vector cross-product is another form of vector multiplication and results in another vector. In this tutorial I show you a simple way of calculating the cross product of two vectors.
From playlist Introducing linear algebra
Exceptional holonomy and related geometric structures: Basic theory - Simon Donaldson
Marston Morse Lectures Topic: Exceptional holonomy and related geometric structures: Basic theory. Speaker: Simon Donaldson Affiliation: Stonybrook University Date: April 3, 2018 For more videos, please visit http://video.ias.edu
From playlist Mathematics
Some recent developments in Kähler geometry and exceptional holonomy – Simon Donaldson – ICM2018
Plenary Lecture 1 Some recent developments in Kähler geometry and exceptional holonomy Simon Donaldson Abstract: This article is a broad-brush survey of two areas in differential geometry. While these two areas are not usually put side-by-side in this way, there are several reasons for d
From playlist Plenary Lectures
Calculus III Exam I Review pt 2
From playlist Calculus III Exam I Review
Henry Adams (8/30/21): Vietoris-Rips complexes of hypercube graphs
Questions about Vietoris-Rips complexes of hypercube graphs arise naturally from problems in genetic recombination, and also from Kunneth formulas for persistent homology with the sum metric. We describe the homotopy types of Vietoris-Rips complexes of hypercube graphs at small scale param
From playlist Beyond TDA - Persistent functions and its applications in data sciences, 2021
Orientations for Moduli Spaces in Higher-Dimensional Gauge Theory by Markus Upmeier
DISCUSSION MEETING ANALYTIC AND ALGEBRAIC GEOMETRY DATE:19 March 2018 to 24 March 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore. Complex analytic geometry is a very broad area of mathematics straddling differential geometry, algebraic geometry and analysis. Much of the interactions be
From playlist Analytic and Algebraic Geometry-2018
Matthew Hastings - Building Manifolds from Error Correcting Codes - IPAM at UCLA
Recorded 02 September 2021. Matthew Hastings of Microsoft Research presents "Building Manifolds from Error Correcting Codes" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. Learn more online at: http://www.ipam.ucla.edu/programs/summer-schools/graduate-summer
From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter
What is a Tensor? Lesson 23: Operations on p-forms. The Exterior Algebra.
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From playlist What is a Tensor?
Pierrick Bousseau - The Skein Algebra of the 4-punctured Sphere from Curve Counting
The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the SL_2 character of a topological surface. I will explain how to realize the skein algebra of the 4-punctured sphere as the output of a mirror symmetry construction based on higher genus Gromov-Wi
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Lecture 18 (CEM) -- Plane Wave Expansion Method
This lecture steps the student through the formulation and implementation of the plane wave expansion method. It describes how to construct electromagnetic band diagrams and isofrequency contours. As bonus sections, it describes how to handle band crossing, how to implement the efficient
From playlist UT El Paso: CEM Lectures | CosmoLearning.org Electrical Engineering
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From playlist Riemannian Geometry Past, Present and Future: an homage to Marcel Berger
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From playlist Physics