File:Vector_add_scale.svg · Wikimedia Commons · See Wikimedia Commons
向量空间
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the basic algebraic structure of linear algebra; a module over a field, such that its elements can be added together or scaled by elements of the field
A vector space is a mathematical structure where you can add elements together or scale them by numbers, and these operations follow consistent rules. It's fundamental to linear algebra and appears throughout mathematics, physics, and engineering because many real-world problems—from computer graphics to machine learning—can be understood through this framework.
AI-generated from the Wikipedia summary — may contain errors.
Wikidata facts
- Subclass of
- free module
- Has part
- scalar multiplication
- Named after
- Euclidean vector
- Image
- Vector add scale.svg
Show 9 more facts
- on focus list of Wikimedia project
- Wikipedia:Vital articles/Level/4
- Commons category
- Vector spaces
- topic's main category
- Category:Vector spaces
- facet of
- linear algebra
- studied by
- linear algebra
- different from
- linear space
- Stack Exchange tag
- math.stackexchange.com/tags/vector-spaces
- maintained by WikiProject
- WikiProject Mathematics
- has characteristic
- dimension of a vector space
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Article · 中文
向量空間是现代数学中的一个基本概念，是線性代數研究的基本对象，是指一組向量及相关的運算即向量加法，純量乘法，以及对運算的一些限制如封闭性，结合律。 在现代数学中，向量的概念不仅限于此，满足下列公理的任何数学对象都可被当作向量处理。譬如，實系數多項式的集合在定义适当的运算后构成向量空間，在代数上处理是方便的。单变元实函数的集合在定义适当的运算后，也构成向量空间，研究此类函数向量空间的数学分支称为泛函分析。
Abstract from DBpedia / Wikipedia · CC BY-SA
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