Vectors (mathematics and physics) | Linear algebra

Coordinate vector

In linear algebra, a coordinate vector is a representation of a vector as an ordered list of numbers (a tuple) that describes the vector in terms of a particular ordered basis. An easy example may be a position such as (5, 2, 1) in a 3-dimensional Cartesian coordinate system with the basis as the axes of this system. Coordinates are always specified relative to an ordered basis. Bases and their associated coordinate representations let one realize vector spaces and linear transformations concretely as column vectors, row vectors, and matrices; hence, they are useful in calculations. The idea of a coordinate vector can also be used for infinite-dimensional vector spaces, as addressed below. (Wikipedia).

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The Unit Vector (2D)

This video explains how to determine a unit vector given a vector. It also explains how to determine the component form of a vector in standard position that intersects the unit circle. http://mathispower4u.yolasite.com/

From playlist Vectors

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What is the formula for component form of a vector

http://www.freemathvideos.com in this video series I will show you how to find the angle of a vector when given in component form or as a linear combination. To understand the direction of a vector it is important to go back to the unit circle and determine how we can find the angle when

From playlist Vectors

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Ex: Identifying the Coordinates of Points on the Coordinate Plane

This video explains how to determine the coordinates of points on the coordinate plane. Complete Video List at http://www.mathispower4u.com Search by Topic at http://www.mathispower4u.wordpress.com

From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables

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Ex: Find a Unit Vector in the Direction of a Given Vector in 3D

This example explains how to find a unit vector in the direction of a given vector in space. Site: http://mathispower4u.com

From playlist Vectors in Space (3D)

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Ex: Find the Magnitude of a Vector in 3D

This video explains how to determine the magnitude of a vector in 3D. Site: http://mathispower4u.com

From playlist Vectors in Space (3D)

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Calculus 3: Vector Calculus in 2D (17 of 39) What is the Position Vector?

Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is the position vector. The position vector indicates the position of a particle relative to the origin. The position usually depends on, or is a function of, a parametric variable (ex. t

From playlist CALCULUS 3 CH 3 VECTOR CALCULUS

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What is the formula for a unit vector from a vector in component form

http://www.freemathvideos.com In this video series I will show you how to find the unit vector when given a vector in component form and as a linear combination. A unit vector is simply a vector with the same direction but with a magnitude of 1 and an initial point at the origin. It is i

From playlist Vectors

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Vectors in Space

This video explains how to sketch vectors in R^3, how to determine the magnitude of a vector and how to determine a unit vector. http://mathispower4u.yolasite.com/

From playlist Vectors

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What is a linear combination of your unit vectors

http://www.freemathvideos.com In this video series I will show you how to find the unit vector when given a vector in component form and as a linear combination. A unit vector is simply a vector with the same direction but with a magnitude of 1 and an initial point at the origin. It is i

From playlist Vectors - Understanding

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Introduction to Change of Basis

This video introduces a change of basis and show how to convert between the standard basis and a nonstandard basis coordinates.

From playlist Vectors: Change of Basis

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Einstein's General Theory of Relativity | Lecture 5

Lecture 5 of Leonard Susskind's Modern Physics concentrating on General Relativity. Recorded October 20, 2008 at Stanford University. This Stanford Continuing Studies course is the fourth of a six-quarter sequence of classes exploring the essential theoretical foundations of modern phys

From playlist Lecture Collection | Modern Physics: Einstein's Theory

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What is General Relativity? Lesson 43: Holonomic and Non-Holonomic Basis

What is General Relativity? Lesson 43: Holonomic and Non-Holonomic Basis Since we have already discussed coordinate systems, basis vectors, and commutator, now is as good a time as any to talk about how 4 arbitrary vector fields may or may not be tangent vectors to coordinate curves. That

From playlist What is General Relativity?

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What is a Tensor 15: Coordinate Transformations

What is a Tensor 15: Coordinate Transformations

From playlist What is a Tensor?

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WildLinAlg12: Generalized dilations and eigenvectors

This video introduces the important idea of changing coordinates in Linear Algebra. A linear transformation can be described using many different matrices, depending on the underlying coordinate system, or ordered basis, which is used to describe the space. The simplest case is when the

From playlist A first course in Linear Algebra - N J Wildberger

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What is General Relativity? Lesson 54 - Scalar Curvature Part 3: Riemann Normal Coordinates

What is General Relativity? Lesson 54 -Scalar Curvature Part 3 Riemann Normal Coordinates This is the second of a few lectures about the Scalar Curvature and its interpretation. The goal is to get us to a point where we can have an interpretation of the Einstein Tensor and therefore an i

From playlist What is General Relativity?

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Tensor Calculus 3a: The Covariant Basis

This course will eventually continue on Patreon at http://bit.ly/PavelPatreon Textbook: http://bit.ly/ITCYTNew Errata: http://bit.ly/ITAErrata McConnell's classic: http://bit.ly/MCTensors Table of Contents of http://bit.ly/ITCYTNew Rules of the Game Coordinate Systems and the Role of Te

From playlist Introduction to Tensor Calculus

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Change of basis | Chapter 13, Essence of linear algebra

How do you translate back and forth between coordinate systems that use different basis vectors? Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Future series

From playlist Essence of linear algebra

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What is General Relativity? Lesson 53: Scalar Curvature Part 2 - The Tetrad Formalism

What is General Relativity? Lesson 53: Scalar Curvature Part 2 - The Tetrad Formalism In this lecture we introduce the tetrad formalism. This is a pre-requisite, in my opinion, to the study of Riemann Normal Coordinates, although RNC are not always introduced with the tetrad formalism in

From playlist What is General Relativity?

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How do you understand the direction of an angle

Learn how to determine the magnitude and direction of a vector. The magnitude of a vector is the length of the vector. The magnitude of a vector is obtained by taking the square root of the sum of the squares of the components of the vector. The direction of a vector is obtained by taking

From playlist Vectors

Related pages

Inverse function | Dimension (vector space) | Tuple | Transpose | Pauli matrices | Linear algebra | Vector space | Field (mathematics) | Change of basis | Vector (mathematics and physics) | Spin (physics) | Linear combination | Matrix (mathematics) | Automorphism | Sequence | Invertible matrix | Isomorphism