In mathematics, specifically in order theory and functional analysis, an abstract m-space or an AM-space is a Banach lattice whose norm satisfies for all x and y in the positive cone of X. We say that an AM-space X is an AM-space with unit if in addition there exists some u ≥ 0 in X such that the interval [−u, u] := { z ∈ X : −u ≤ z and z ≤ u } is equal to the unit ball of X; such an element u is unique and an order unit of X. (Wikipedia).

What is a Vector Space? (Abstract Algebra)

Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su

From playlist Abstract Algebra

A WEIRD VECTOR SPACE: Building a Vector Space with Symmetry | Nathan Dalaklis

We'll spend time in this video on a weird vector space that can be built by developing the ideas around symmetry. In the process of building a vector space with symmetry at its core, we'll go through a ton of different ideas across a handful of mathematical fields. Naturally, we will start

From playlist The New CHALKboard

This video explains the definition of a vector space and provides examples of vector spaces.

From playlist Vector Spaces

What is a Vector Space? Definition of a Vector space.

From playlist Linear Algebra

The formal definition of a vector space.

From playlist Linear Algebra Done Right

Now we know about vector spaces, so it's time to learn how to form something called a basis for that vector space. This is a set of linearly independent vectors that can be used as building blocks to make any other vector in the space. Let's take a closer look at this, as well as the dimen

From playlist Mathematics (All Of It)

This lecture is on Introduction to Higher Mathematics (Proofs). For more see http://calculus123.com.

From playlist Proofs

33 - The dimension of a vector space

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

From playlist Algebra 1M

MAST30026 Lecture 1: What is space? (Part 1)

I started with three dictionary definitions of "space" and briefly discussed them, before moving on to a survey of the standard abstract notions of space used in mathematics, including metric, topological and Hilbert spaces. In the remainder of the lecture I discussed the connection betwee

From playlist MAST30026 Metric and Hilbert spaces

algebraic geometry 21 Projective space bundles

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers projective space bundles, with Hirzebruch surfaces and scrolls as examples. It also includes a brief discussion of abstract varieties. Typo: in the definition o

From playlist Algebraic geometry I: Varieties

Stefaan Vaes: Cohomology and L2-Betti numbers for subfactors and quasi-regular inclusions

Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b

From playlist Analysis and its Applications

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

From playlist Algebra 1M

Lecture 3 | The Theoretical Minimum

January 23, 2012 - In this course, world renowned physicist, Leonard Susskind, dives into the fundamentals of classical mechanics and quantum physics. He discovers the link between the two branches of physics and ultimately shows how quantum mechanics grew out of the classical structure. I

From playlist Lecture Collection | The Theoretical Minimum: Quantum Mechanics

Ivan Todorov: Morita equivalence for operator systems

Talk in Global Noncommutative Geometry Seminar (Europe), 26 January 2022

From playlist Global Noncommutative Geometry Seminar (Europe)

Lecture 2 | Quantum Entanglements, Part 1 (Stanford)

Lecture 2 of Leonard Susskind's course concentrating on Quantum Entanglements (Part 1, Fall 2006). Recorded October 2, 2006 at Stanford University. This Stanford Continuing Studies course is the first of a three-quarter sequence of classes exploring the "quantum entanglements" in modern

From playlist Course | Quantum Entanglements: Part 1 (Fall 2006)

Twisted generating functions and the nearby Lagrangian conjecture - Sylvain Courte

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Topic: Twisted generating functions and the nearby Lagrangian conjecture Speaker: Sylvain Courte Affiliation: Université Grenoble Alpes Date: February 26, 2021 For more video please visit http://video.ias.edu Courte-2021-02

From playlist Mathematics

What is a Module? (Abstract Algebra)

A module is a generalization of a vector space. You can think of it as a group of vectors with scalars from a ring instead of a field. In this lesson, we introduce the module, give a variety of examples, and talk about the ways in which modules and vector spaces are different from one an

From playlist Abstract Algebra

Math 060 Fall 2017 110817C Inner Product Spaces 1

Definition of inner product space. Examples. Definitions: orthogonal, norm, vector projection, scalar projection. Pythagorean theorem (in inner product space).

From playlist Course 4: Linear Algebra (Fall 2017)

Today, we begin the manifolds series by introducing the idea of a topological manifold, a special type of topological space which is locally homeomorphic to Euclidean space.

From playlist Manifolds