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).
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
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
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
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
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
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
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
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
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
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
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
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)
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
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
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)
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
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