File:3d_two_bases_same_vector.svg · Wikimedia Commons · See Wikimedia Commons
base
Sign in to saveAlso known as Hamel basis, algebraic basis, basis of a vector space, vector basis
subset of a vector space that allows defining coordinates
A basis is a minimal set of vectors in a vector space that can be combined together to create any other vector in that space, much like how a few basic ingredients can be mixed to make many different dishes. It matters because having a basis lets mathematicians and scientists assign coordinates to vectors, making it easier to perform calculations and understand the structure of complex mathematical spaces.
AI-generated from the Wikipedia summary — may contain errors.
In the Vinony graph
Vinony's link graph records 674 inbound references to base, and connects out to linear independence, affine space and differential form.
It sits within the topics Axiom of choice and Linear algebra.
Vinony links it to 50 Wikipedia language editions.
Wikidata facts
- Named after
- Georg Hamel
Show 6 more facts
- Commons category
- Basis (linear algebra)
- has characteristic
- linear independence
- facet of
- linear algebra
- studied by
- linear algebra
- opposite of
- Schauder basis
- maintained by WikiProject
- WikiProject Mathematics
Sources (3)
via Wikidata · CC0
Article · Español
En álgebra lineal, una base de un espacio vectorial sobre un campo es un subconjunto de y cumple las siguientes condiciones: * Todos los elementos de pertenecen al espacio vectorial . * Los elementos de forman un sistema linealmente independiente. * Todo elemento de V se puede escribir como combinación lineal de los elementos de la base (es decir, es un sistema generador de ).
Abstract from DBpedia / Wikipedia · CC BY-SA