Abstract algebra

Direct product

In mathematics, one can often define a direct product of objects already known, giving a new one. This generalizes the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one talks about the product in category theory, which formalizes these notions. Examples are the product of sets, groups (described below), rings, and other algebraic structures. The product of topological spaces is another instance. There is also the direct sum – in some areas this is used interchangeably, while in others it is a different concept. (Wikipedia).

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Direct Products of Groups (Abstract Algebra)

The direct product is a way to combine two groups into a new, larger group. Just as you can factor integers into prime numbers, you can break apart some groups into a direct product of simpler groups. Be sure to subscribe so you don't miss new lessons from Socratica: http://bit.ly/1ixuu

From playlist Abstract Algebra

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Inner products (video 3): Definition

Recordings of the corresponding course on Coursera. If you are interested in exercises and/or a certificate, have a look here: https://www.coursera.org/learn/pca-machine-learning

From playlist Inner Products

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Introduction to the Dot Product

Introduction to the Dot Product If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)

From playlist Calculus 3

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Building A Product From The Ground Up

For most seasoned business owners and aspiring entrepreneurs, the product development process often carries a mystical aura. Product development refers to the complete process of taking a product to market. It also covers renewing an existing product and introducing an old product to a new

From playlist Product Development

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Visual Group Theory, Lecture 3.4: Direct products

Visual Group Theory, Lecture 3.4: Direct products There is a natural way to put a group structure on the Cartesian product of two groups. In this lecture, we introduce this concept algebraically, and show several different ways to visualize this, using tools such as Cayley diagrams and mu

From playlist Visual Group Theory

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Abstract Algebra - 8.1 External Direct Products

Let's explore how we can create new groups using existing groups. We do that by essentially creating the cartesian product of the existing groups. We look at the properties associated with these products and delve into how to show isomorphisms between an external direct product and existin

From playlist Abstract Algebra - Entire Course

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A Concrete Introduction to Tensor Products

The tensor product of vector spaces (or modules over a ring) can be difficult to understand at first because it's not obvious how calculations can be done with the elements of a tensor product. In this video we give an explanation of an explicit construction of the tensor product and work

From playlist Tensor Products

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GT21. Internal Products

Abstract Algebra: We consider conditions for when a group is isomorphic to a direct or semidirect product. Examples include groups of order 45, 21, and cyclic groups Z/mn, where m,n are relatively prime. U.Reddit course materials available at http://ureddit.com/class/23794/intro-to-grou

From playlist Abstract Algebra

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Inner products (video 8): Outro

Recordings of the corresponding course on Coursera. If you are interested in exercises and/or a certificate, have a look here: https://www.coursera.org/learn/pca-machine-learning

From playlist Inner Products

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Martin Bridson - Subgroups of direct products of surface groups

After reviewing what is known about subgroups of direct products of surface groups and their significance in the story of which groups are Kähler, I shall describe a new construction that provides infinite families of finitely presented subgroups. These subgroups have varying higher-finite

From playlist Geometry in non-positive curvature and Kähler groups

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Linear Algebra for Computer Scientists. 5. Dot Product of Two Vectors

This computer science video is the fifth in a series about linear algebra for computer scientists. In this video you will learn how to calculate the dot product of two vectors, and why you might want to do it. You will see that the dot product of two vectors (also known as the inner prod

From playlist Linear Algebra for Computer Scientists

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ME564 Lecture 21: Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product

ME564 Lecture 21 Engineering Mathematics at the University of Washington Linear algebra in 2D and 3D: inner product, norm of a vector, and cross product Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L21.pdf Course Website: http://faculty.washington.edu/sbrunton/me564/ http:/

From playlist Engineering Mathematics (UW ME564 and ME565)

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Abstract Algebra - 9.3 Internal Direct Products

We finish up Chapter 9 by studying internal direct products, which are "shockingly" isomorphic to external direct products despite that the elements themselves are structured differently. Video Chapters: Intro 0:00 What is an Internal Direct Product 0:05 More Isomorphisms 3:51 External vs

From playlist Abstract Algebra - Entire Course

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Cross Product Torque (with a Cross Product Review)

Torque as the cross product is introduced. How to actually perform the cross product using matrices is reviewed and 4.5 examples are walked through. Want Lecture Notes? http://www.flippingphysics.com/torque-cross-product.html This is an AP Physics C: Mechanics topic. Content Times: 0:00 T

From playlist Rotational Dynamics - AP Physics C: Mechanics

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Lecture 03: Vector Calculus (P)Review (CMU 15-462/662)

Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz2emSh0UQ5iOdT2xRHFHL7E Course information: http://15462.courses.cs.cmu.edu/

From playlist Computer Graphics (CMU 15-462/662)

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Calculus 3: Vector Calculus in 3-D (24 of 35) A Real World Example of a Cross Product

Visit http://ilectureonline.com for more math and science lectures! In this video I will find give a real-world example of using cross-product or vector-product. I will find force, F=?, on a positive charge moving at velocity=v across a magnetic field B. Next video in the series can be s

From playlist CALCULUS 3 CH 3.3 VECTOR CALCULUS IN 3-D

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Cross product of vectors

What is the cross product of two vectors? How is it useful? Free ebook https://bookboon.com/en/introduction-to-vectors-ebook (updated link) Test your understanding via a short quiz http://goo.gl/forms/Ii3hPtwksX

From playlist Introduction to Vectors

Related pages

Topological space | Metric space | Symmetric relation | Direct sum of modules | Topology | Coproduct | Up to | Isomorphism | Group (mathematics) | Trivial group | Connected relation | Indexed family | Tensor product of modules | Product (category theory) | Binary relation | Transitive relation | Preorder | Reflexive relation | Mathematics | Set (mathematics) | Field (mathematics) | Semidirect product | Direct sum of groups | Euclidean space | Normal subgroup | Cartesian product | Category theory | Ring (mathematics) | Morphism | Signature (logic) | Direct sum | Tychonoff's theorem | Equivalence relation | Tuple | Group homomorphism | Antisymmetric relation | Abelian group | Box topology | Product topology | Module (mathematics) | Multiplicative inverse