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Concept

Vector Space

Also Known As Linear Space
Algebra

A vector space, also called a linear space, is a set whose elements, called vectors, can be added together and multiplied by numbers called scalars, subject to a fixed set of axioms governing those two operations. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Origin Year
1888 1
Connections

Associated With

Eigenvalues and Eigenvectors, Concepts

Eigenvectors are defined as vectors of a vector space whose direction a linear transformation leaves unchanged, so the concept is defined on top of the vector space concept.

Additional Source Eigenvalues and Eigenvectors (Wikipedia)Lead section
Tensor, Concepts

A tensor is defined as a multilinear relationship between sets of algebraic objects associated with a vector space, so the concept is built directly on the vector space concept.

Additional Source Tensor (Wikipedia)Lead section

Attributed To

Henri Lebesgue, Mathematicians
Source Vector Space (Wikipedia)
Stefan Banach, Mathematicians
Source Vector Space (Wikipedia)

In Branch

Algebra, Branches of Mathematics
Source Vector Space (Wikipedia)
Functional Analysis, Branches of Mathematics
Linear Algebra, Branches of Mathematics
Source Vector Space (Wikipedia)
Sources
1. Vector Space (Wikipedia)
Wikimedia Foundation
  • lead paragraph
    A vector space (also called a linear space) is a set whose elements, often called vectors, can be added together and multiplied ("scaled") by numbers called scalars.
  • History
    Italian mathematician Peano was the first to give the modern definition of vector spaces and linear maps in 1888, although he called them "linear systems".
  • Attributed To: Henri Lebesgue, Lead
    An important development of vector spaces is due to the construction of function spaces by Henri Lebesgue
  • Attributed To: Stefan Banach, Lead
    Banach spaces, introduced by Stefan Banach, are complete normed vector spaces
View the Source
Eigenvalues and Eigenvectors (Wikipedia)
Wikimedia FoundationAssociated With: Eigenvalues and Eigenvectors, Lead section
Quote, Associated With: Eigenvalues and Eigenvectors, Lead section
In linear algebra, an eigenvector ( EYE-gən-) or characteristic vector is a (nonzero) vector that has its direction unchanged (or reversed) by a given linear transformation.
View the Source
Tensor (Wikipedia)
Wikimedia FoundationAssociated With: Tensor, Lead section
Quote, Associated With: Tensor, Lead section
a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space
View the Source

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