在数学中，赋范矢量空间是具有“长度”概念的矢量空间。是通常的欧几里得空间 R 的推广。R中的长度被更抽象的范数替代。“长度”概念的特征是：

一个把矢量映射到非负实数的函数如果满足以上性质，就叫做一个半范数；如果只有零矢量的函数值是零，那幺叫做范数。拥有一个范数的矢量空间叫做赋范矢量空间，拥有半范数的叫做半赋范矢量空间。

In mathematics, with 2- or 3-dimensional vectors with real-valued entries, the idea of the "length" of a vector is intuitive and can easily be extended to any real vector space R. The following properties of "vector length" are crucial.

The generalization of these three properties to more abstract vector spaces leads to the notion of norm. A vector space on which a norm is defined is then called a normed space or normed vector space. Normed vector spaces are central to the study of linear algebra and functional analysis.