Lemmas in linear algebra | Matroid theory
The Steinitz exchange lemma is a basic theorem in linear algebra used, for example, to show that any two bases for a finite-dimensional vector space have the same number of elements. The result is named after the German mathematician Ernst Steinitz. The result is often called the Steinitz–Mac Lane exchange lemma, also recognizing the generalizationby Saunders Mac Laneof Steinitz's lemma to matroids. (Wikipedia).
Equivalence Relations Definition and Examples
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Equivalence Relations Definition and Examples. This video starts by defining a relation, reflexive relation, symmetric relation, transitive relation, and then an equivalence relation. Several examples are given.
From playlist Abstract Algebra
35 - Properties of bases (continued)
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Isomorphisms (Abstract Algebra)
An isomorphism is a homomorphism that is also a bijection. If there is an isomorphism between two groups G and H, then they are equivalent and we say they are "isomorphic." The groups may look different from each other, but their group properties will be the same. Be sure to subscribe s
From playlist Abstract Algebra
Linear Algebra - Part 26 - Steinitz Exchange Lemma
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From playlist Linear Algebra
Linear Algebra - Part 26 - Steinitz Exchange Lemma [dark version]
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From playlist Linear Algebra [dark version]
Jeff Erickson - Lecture 5 - Two-dimensional computational topology - 22/06/18
School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects (http://geomschool2018.univ-mlv.fr/) Jeff Erickson (University of Illinois at Urbana-Champaign, USA) Two-dimensional computational topology - Lecture 4 Abstract: This series of lectures will describe recent
From playlist Jeff Erickson - School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects
Isomorphisms in abstract algebra
In this video I take a look at an example of a homomorphism that is both onto and one-to-one, i.e both surjective and injection, which makes it a bijection. Such a homomorphism is termed an isomorphism. Through the example, I review the construction of Cayley's tables for integers mod 4
From playlist Abstract algebra
Lecture 16: Vertex & Orthogonal Unfolding
MIT 6.849 Geometric Folding Algorithms: Linkages, Origami, Polyhedra, Fall 2012 View the complete course: http://ocw.mit.edu/6-849F12 Instructor: Erik Demaine This lecture continues with open problems involving general unfoldings of polyhedra and proof of vertex unfolding using constructi
From playlist MIT 6.849 Geometric Folding Algorithms, Fall 2012
51 - Properties of Ker(T) and Im(T)
Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering
From playlist Algebra 1M
Emmy Noether in Erlangen and Göttingen by Ravi Rao
DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016 VENUE: Madhava Lecture Hall, ICTS Bangalore Emmy Noether (1882-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (
From playlist The Legacy of Emmy Noether
Abstract Algebra | Equivalence Relations
We give the definition of an equivalence relation and some examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Abstract Algebra
(New Version Available) Inverse Functions
New Version: https://youtu.be/q6y0ToEhT1E Define an inverse function. Determine if a function as an inverse function. Determine inverse functions. http://mathispower4u.wordpress.com/
From playlist Exponential and Logarithmic Expressions and Equations
How to evaluate for the composition of two trigonometric functions
👉 Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
Introduction to Relations and Functions (L9.1)
This lesson introduces functions and explains how to determine if a relations is a function. The vertical line also used. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Introduction to Functions: Function Basics
Determine if a Relation Given as a Table is a One-to-One Function
This video will explain how to determine if a relations given as a table is a one to one function. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Determining Inverse Functions
23 Algebraic system isomorphism
Isomorphic algebraic systems are systems in which there is a mapping from one to the other that is a one-to-one correspondence, with all relations and operations preserved in the correspondence.
From playlist Abstract algebra
Topological transcendence degree - M. Temkin - Workshop 2 - CEB T1 2018
Michael Temkin (Hebrew University) / 06.03.2018 Topological transcendence degree. My talk will be devoted to a basic theory of extensions of complete real-valued fields L/K. Naturally, one says that L is topologically-algebraically generated over K by a subset S if L lies in the completi
From playlist 2018 - T1 - Model Theory, Combinatorics and Valued fields
Put all three properties of binary relations together and you have an equivalence relation.
From playlist Abstract algebra