Real numbers | Analytic geometry | Mathematical analysis | Topological vector spaces | Multivariable calculus
In mathematics, the real coordinate space of dimension n, denoted Rn (/ɑːrˈɛn/ ar-EN) or , is the set of the n-tuples of real numbers, that is the set of all sequences of n real numbers. With component-wise addition and scalar multiplication, it is a real vector space, and its elements are called coordinate vectors. The coordinates over any basis of the elements of a real vector space form a real coordinate space of the same dimension as that of the vector space. Similarly, the Cartesian coordinates of the points of a Euclidean space of dimension n form a real coordinate space of dimension n. These one to one correspondences between vectors, points and coordinate vectors explain the names of coordinate space and coordinate vector. It allows using geometric terms and methods for studying real coordinate spaces, and, conversely, to use methods of calculus in geometry. This approach of geometry was introduced by René Descartes in the 17th century. It is widely used, as it allows locating points in Euclidean spaces, and computing with them. (Wikipedia).
Dual spaces and linear functionals In this video, I introduce the concept of a dual space, which is the analog of a "shadow world" version, but for vector spaces. I also give some examples of linear and non-linear functionals. This seems like an innocent topic, but it has a huge number of
From playlist Dual Spaces
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
The formal definition of a vector space.
From playlist Linear Algebra Done Right
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
Space Coordinates Plotting Points in 3 Dimensions
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Space Coordinates Plotting Points in 3 Dimensions
From playlist Calculus 3
Three-Dimensional Coordinates and the Right-Hand Rule
We've done tons of stuff with the coordinate plane, but that depicts only two spatial dimensions. We experience the world in three spatial dimensions, so sometimes we will need to communicate coordinates in three-dimensional space. Let's look at some rules regarding this system, and a few
From playlist Mathematics (All Of It)
What exactly is space? Brian Greene explains what the "stuff" around us is. Subscribe to our YouTube Channel for all the latest from World Science U. Visit our Website: http://www.worldscienceu.com/ Like us on Facebook: https://www.facebook.com/worldscienceu Follow us on Twitter: https:
From playlist Science Unplugged: Physics
This video is about The Coordinate Plane
From playlist Integers and The Coordinate Plane
Lie Groups and Lie Algebras: Lesson 14 - Continuous Groups of Transformations
Lie Groups and Lie Algebra: Lesson 14 - Continuous Groups of Transformations We connect the idea of a continuous group to the idea of transforming the bases of a vector space. Please consider supporting this channel via Patreon: https://www.patreon.com/XYLYXYLYX
From playlist Lie Groups and Lie Algebras
What is General Relativity? Special Lecture: Tangent Spaces and Coordinate Basis
What is General Relativity? Special Lecture: Tangent Spaces and Coordinate Basis This is a LONG lecture covering a narrow but important topic: tangent spaces and the coordinate basis. It is intended for anyone who has trouble understanding why a manifold has a vector space at every point
From playlist What is a Manifold?
What is a Manifold? Lesson 8: Diffeomorphisms
What is a Manifold? Lesson 8: Diffeomorphisms
From playlist What is a Manifold?
What is a Tensor 14: Vector and Tensor Fields
What is a Tensor 14: Vector and Tensor Fields
From playlist What is a Tensor?
What is a Manifold? Lesson 11: The Cotangent Space
What is a Manifold? Lesson 11: The Cotangent Space I have annotated an obvious error at 2:00. However annotations are not visible on mobile devices!
From playlist What is a Manifold?
What is a Tensor 13: Realization of a Vector Space
What is a Tensor 13: Realization of a Vector Space Note: There is an error at 3:26. The equality I write down is only true for orthonormal basis vectors! There will always be a relationship between (e_\mu, e_\nu) and (e^\mu , e^\nu) but it wont always be as simple as I wrote down! For som
From playlist What is a Tensor?
What is a Tensor? Lesson 16: The metric tensor field
What is a Tensor? Lesson 16: The metric tensor field
From playlist What is a Tensor?
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co
From playlist Lie Groups and Lie Algebras
Lie Groups and Lie Algebras: Lesson 18- Group Generators
Lie Groups and Lie Algebras: Lesson 18- Generators This is an important lecture! We work through the calculus of *group generators* and walk step-by-step through the exploitation of analyticity. That is, we use the Taylor expansion of the continuous functions associated with a Lie group o
From playlist Lie Groups and Lie Algebras
Lec 4 - Phys 237: Gravitational Waves with Kip Thorne
Watch the rest of the lectures on http://www.cosmolearning.com/courses/overview-of-gravitational-wave-science-400/ Redistributed with permission. This video is taken from a 2002 Caltech on-line course on "Gravitational Waves", organized and designed by Kip S. Thorne, Mihai Bondarescu and
From playlist Caltech: Gravitational Waves with Kip Thorne - CosmoLearning.com Physics
The Equations of the Coordinate Planes in R3
This video identifies the three coordinate planes in the 3D coordinate system. Site: http://mathispower4u.com
From playlist Equations of Planes and Lines in Space