Linear algebra | Binary relations

Dependence relation

In mathematics, a dependence relation is a binary relation which generalizes the relation of linear dependence. Let be a set. A (binary) relation between an element of and a subset of is called a dependence relation, written , if it satisfies the following properties: * if , then ; * if , then there is a finite subset of , such that ; * if is a subset of such that implies , then implies ; * if but for some , then . Given a dependence relation on , a subset of is said to be independent if for all If , then is said to span if for every is said to be a basis of if is independent and spans Remark. If is a non-empty set with a dependence relation , then always has a basis with respect to Furthermore, any two bases of have the same cardinality. (Wikipedia).

Video thumbnail

The Purpose of Friendship

Our desire to build good and lasting friendships is often undermined by a lack of focus on what friendship should really be about. Getting clear about what friendship is for isn’t cynical; it provides the foundation for genuine bonds. If you like our films, take a look at our shop (we shi

From playlist RELATIONSHIPS

Video thumbnail

What is Transference And Why It Matters

Transference is a psychological phenomenon whereby we ‘transfer’ a way of behaving from childhood into adulthood – in situations which don’t really warrant it. It’s a big cause of trouble in relationships. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/U

From playlist RELATIONSHIPS

Video thumbnail

What Infidelity Means

Being a victim of infidelity is one of the worst things that can befall us in love. One of the ways to come back from the harrowing experience is to ask what the real meaning of the infidelity might be. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/yW1

From playlist RELATIONSHIPS

Video thumbnail

Gravitation (3 of 17) Mass vs Weight, An Explanation

Explains the difference between mass and weight. Very important. No they are not the same thing. Mass is a measure of the amount "stuff" something is made of, the amount of atoms for example. Weight is a measure of the force of attraction between two object that have mass. Of course mass

From playlist Gravitation: Orbital Velocity, Orbital Period, Potential Energy, Kinetic Energy, Mass and Weight

Video thumbnail

How to Prove a Relation is an Equivalence Relation

How to Prove a Relation is an Equivalence Relation Proving a Relation is Reflexive, Symmetric, and Transitive;i.e., an equivalence relation. I had never done this problem before so there are moments where you can see me pause briefly because I had to figure it out.

From playlist Functions, Sets, and Relations

Video thumbnail

Friendship & Vulnerability

We often think that the best way to have friends is to be deeply impressive and accomplished. In fact, the route to true friendship always flows through vulnerability. If you like our films take a look at our shop (we ship worldwide): http://www.theschooloflife.com/shop/all/ Brought to you

From playlist RELATIONSHIPS

Video thumbnail

Mod-02 Lec-04 Carvaka Philosophy - II

Indian Philosophy by Dr. Satya Sundar Sethy, Department of Humanities and Social Sciences, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

From playlist IIT Madras: Introduction to Indian Philosophy | CosmoLearning.org Philosophy

Video thumbnail

Reinaldo Funes Monzote: Sugar Cane and Agricultural Transformations in Cuba

Reinaldo Funes Monzote is at Yale as the Henry Hart Rice Family Foundation Visiting Professor at the MacMillan Center. He is Associate Professor of History at the University of Havana, Cuba. He is the author of "From Rainforest to Cane Field in Cuba," the award-winning environmental histor

From playlist The MacMillan Report

Video thumbnail

UHCL 30a Graduate Database Course - Bernsteins Synthesis Algorithm

This video corresponds to the unit 6 notes for a graduate database (dbms) course taught by Dr. Gary D. Boetticher at the University of Houston - Clear Lake (UHCL). The theme is relational database theory. This video focuses on how to convert a relation schema to third normal form using Ber

From playlist UHCL Graduate Database Course

Video thumbnail

Time-dependent non-Hermitian systems a status update by Andreas Fring

DATE: 04 June 2018 to 13 June 2018 VENUE:Ramanujan Lecture Hall, ICTS Bangalore Non-Hermitian Physics-"Pseudo-Hermitian Hamiltonians in Quantum Physics (PHHQP) XVIII" is the 18th meeting in the series that is being held over the years in Quantum Physics. The scope of the program on Non-H

From playlist Non-Hermitian Physics - PHHQP XVIII

Video thumbnail

Overview - Ravi Sheth

Ravi Sheth - September 24, 2015 http://sns.ias.edu/~baldauf/Bias/index.html The interpretation of low-redshift galaxy surveys is more complicated than the interpretation of CMB temperature anisotropies. First, the matter distribution evolves nonlinearly at low redshift, limiting the use

From playlist Unbiased Cosmology from Biased Tracers

Video thumbnail

O'Reilly Webcast: Nullology: The Zen of Database

Nullology is the study of the empty set. Of course, sets crop up all over the place in the database world; but the question is--and it's a crucial one--what happens if the set under consideration happens to be empty? For example, a relation contains a set of tuples: what about the possibil

From playlist O'Reilly Webcasts

Related pages

Field extension | Binary relation | Algebraic element | Linear independence | Linear subspace | Vector space | Mathematics | Set (mathematics) | Field (mathematics) | Finite set | Logical equivalence | Cardinality | Dependency relation | Matroid | Subset