Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Cartesian Vector Notation01:28

Cartesian Vector Notation

1.8K
Cartesian vector notation is a valuable tool in mechanical engineering for representing vectors in three-dimensional space, performing vector operations such as determining the gradient, divergence, and curl, and expressing physical quantities such as the displacement, velocity, acceleration, and force. By using Cartesian vector notation, engineers can more easily analyze and solve problems in various areas of mechanical engineering, including dynamics, kinematics, and fluid mechanics. This...
1.8K
Vector Algebra: Method of Components01:08

Vector Algebra: Method of Components

20.4K
It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...
20.4K
Vector Algebra: Graphical Method01:10

Vector Algebra: Graphical Method

18.6K
Vectors can be multiplied by scalars, added to other vectors, or subtracted from other vectors. The vector sum of two (or more) vectors is called the resultant vector or, for short, the resultant.
We use the laws of geometry to construct resultant vectors, followed by trigonometry to find vector magnitudes and directions. For a geometric construction of the sum of two vectors in a plane, we follow the parallelogram rule. Suppose two vectors are at arbitrary positions. Translate either one of...
18.6K
Cartesian Form for Vector Formulation01:26

Cartesian Form for Vector Formulation

1.2K
The Cartesian form for vector formulation is a process to calculate  the moment of force using the position and force vectors. The moment of force is defined as the cross-product of these vectors, making it a vector quantity. The Cartesian form of the position and force vectors involves unit vectors, which can be used to express the cross-product in determinant form.
1.2K
Vectors01:30

Vectors

660
Vectors are mathematical entities characterized by both magnitude and direction. Unlike scalars, which are defined solely by magnitude, vectors represent quantities like displacement, velocity, and force, where direction is essential. Vectors are graphically represented as directed line segments, extending from an initial point to a terminal point, denoted with bold letters or arrows placed above the symbol. Two vectors are deemed equal if they share identical magnitudes and directions,...
660
Vector Operations01:20

Vector Operations

2.6K
Vectors are physical quantities that have both magnitude and direction. The vector operations include addition, subtraction, and scalar multiplication.
A vector multiplied by a scalar value is called scalar multiplication. The result obtained is a new vector with a different magnitude. If the scalar is positive, the direction of the vector remains the same, but if it is negative, the direction of the vector is reversed. For example, the product of the mass and velocity yields the momentum.
2.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same journal

A Fast Summation Method for Oscillatory Lattice Sums.

Journal of mathematical physics·2020
Same journal

Influences of degree inhomogeneity on average path length and random walks in disassortative scale-free networks.

Journal of mathematical physics·2020
Same journal

Keyring models: an approach to steerability.

Journal of mathematical physics·2019
Same journal

Optimal decay rates for the compressible viscoelastic flows.

Journal of mathematical physics·2016
Same journal

Existence and asymptotic behavior of solutions for nonlinear Schrödinger-Poisson systems with steep potential well.

Journal of mathematical physics·2016
Same journal

Segregated and synchronized vector solutions to linearly coupled systems of Schrödinger equations.

Journal of mathematical physics·2015

Related Experiment Video

Updated: Mar 26, 2026

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

29.5K

Antisymmetric tensor generalizations of affine vector fields.

Tsuyoshi Houri1, Yoshiyuki Morisawa2, Kentaro Tomoda1

  • 1Department of Physics, Kobe University , 1-1 Rokkodai, Nada, Kobe, Hyogo 657-8501, Japan.

Journal of Mathematical Physics
|February 10, 2016
PubMed
Summary
This summary is machine-generated.

This study explores antisymmetric affine tensor fields, revealing their connection to parallelly transported tensor fields. The research establishes bounds on their number and derives integrability conditions for their existence in spacetimes.

More Related Videos

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

12.0K
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.8K

Related Experiment Videos

Last Updated: Mar 26, 2026

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases
09:33

Diffusion Tensor Magnetic Resonance Imaging in the Analysis of Neurodegenerative Diseases

Published on: July 28, 2013

29.5K
Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section
11:00

Experimental Investigation of Secondary Flow Structures Downstream of a Model Type IV Stent Failure in a 180° Curved Artery Test Section

Published on: July 19, 2016

12.0K
Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
13:44

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

Published on: August 30, 2013

43.8K

Area of Science:

  • Differential Geometry
  • General Relativity
  • Mathematical Physics

Background:

  • Affine vector fields are fundamental in describing symmetries of spacetimes.
  • Symmetric affine tensor fields have been previously investigated for spacetime symmetries.
  • Antisymmetric affine tensor fields represent a less explored area of spacetime symmetry.

Purpose of the Study:

  • To investigate the properties of antisymmetric affine tensor fields.
  • To establish the relationship between antisymmetric affine tensor fields and parallelly transported tensor fields.
  • To determine the conditions for the existence of these tensor fields in various spacetimes.

Main Methods:

  • Reviewing properties of symmetric affine tensor fields.
  • Analyzing the behavior of antisymmetric affine tensor fields.
  • Deriving integrability conditions for antisymmetric affine tensor fields.
  • Investigating the relationship with parallelly transported tensor fields.

Main Results:

  • Antisymmetric affine tensor fields are closely related to parallelly transported lower-rank antisymmetric tensor fields.
  • The number of independent rank-p antisymmetric affine tensor fields in n-dimensions is bounded by (n+1)!/[p!(n-p)!].
  • Integrability conditions for antisymmetric affine tensor fields were derived.

Conclusions:

  • The derived integrability conditions facilitate the discussion on the existence of antisymmetric affine tensor fields.
  • This work provides a foundation for further research into spacetime symmetries described by antisymmetric affine tensor fields.