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In contrast in special relativity, M is taken to be a vector space V (of dimension four).
而狭义相对论中,M被取为一个四维的向量空间V。
Let F(V) be the space of all finite rank linear transformations on a vector space V over a field F.
令V是域F上的向量空间,F(V)是作用于V上的所有有限秩线性变换构成的向量空间。
Theorem 1: The subspace spanned by a non-empty subset S of a vector space V is the set of all linear combinations of vectors in S. This theorem is so well known that at times it is referred to as the definition of span of a set.
定理 1:向量空间 V 的非空集合 S 生成的子空间是 S 中向量的所有有限线性组合; 如注释中所说,这个定理如此熟知,以至有时也作为一个集合的生成空间的定义。
It is a finite-dimensional vector space V with a group action of an algebraic group G, such that there is an orbit of G that is open for the Zariski topology (and so, dense).
它是带有一个代数群 G 作用的有限维向量空间 X ,使得存在G 的一个轨道在扎里斯基拓扑 下是开集(从而稠密 ) 。
Given a vector space V we can take G to be the general linear group GL(V), and X to be the set of all (ordered) bases of V.
给定向量空间 V ,可以将G 取作一般线性群 GL(V ) , 而X 取作所有(有序)基 的集合。
Another example is the affine space concept: the idea of the affine space A underlying a vector space V can be said succinctly by saying that A is a principal homogeneous space for V acting as the additive group of translations.
另外一个例子是仿射空间 的概念:向量空间 V 之下的仿射空间 A 的想法可以简洁地表述为A 是V 作为平移的加法群作用的主齐性空间。
For any n-dimensional real vector space V we can form the kth-exterior power of V, denoted ΛkV.
对任意 n-维实向量空间 V,我们可构造 V 的 k-次外幂,记作 ΛkV。
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