Lemmas in linear algebra | Matroid theory

Steinitz exchange lemma

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).

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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

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35 - Properties of bases (continued)

Algebra 1M - international Course no. 104016 Dr. Aviv Censor Technion - International school of engineering

From playlist Algebra 1M

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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

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Linear Algebra - Part 26 - Steinitz Exchange Lemma

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From playlist Linear Algebra

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Linear Algebra - Part 26 - Steinitz Exchange Lemma [dark version]

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From playlist Linear Algebra [dark version]

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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

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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

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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

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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

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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

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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

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(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

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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

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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

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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

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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

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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

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12 Equivalence relations

Put all three properties of binary relations together and you have an equivalence relation.

From playlist Abstract algebra

Related pages

Computational mathematics | Basis (linear algebra) | Linear independence | Saunders Mac Lane | Dimension (vector space) | Linear span | Vector space | Linear algebra | Numerical linear algebra | Mathematical induction | Ernst Steinitz | Matroid | Mizar system