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.
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