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n-维向量空间（n-dimensional vector space），在解析几何中有些事物的性质不能用一个数来刻画，如一个n元方程组的解是由n个数组成，而这n个数作为方程组的解是一个整体，分开来谈是没有意义的，这时我们就需要用n维向量来刻画方程组的解。 Px, py, pz, mc), where as fifth component the mass of a particle introduced. Theorem 2.11: Every linearly independent list of vectors in a finite-dimensional vector space can be extended to a basis of the vector space 这两条实际上说了，可以张成 向量空间 的一组向量看起来比一组基“大”，而一组线性无关的向量看起来比一组基“小”。
數學 中, 向量空間 V 的 維數 是 V 的基底的 勢，即基底中向量的個數。 向量空間的維數有時也稱作 哈梅爾維數 （Hamel basis）或 代數維數 以便與其他類型的 維數 相區別。 向量空間中的所有基底具有相等的勢（參閱 向量空間的維數定理）。 所以向量空間的維數是唯一併確定的. 若 F 為 體， F 上的向量空間 V 的維數可記為 dim F (V) 或 [V : F], 讀作 " V 在 F 上的維數"。 當上下文中給出明確的 F 時, 通常記為 dim (V) . 向量空間 R3 的 基底 為. 因此 dim R (R3) = 3。 廣泛來講, dim R (Rn) = n。更加廣泛而言, 對任何的 體 F，dim F (Fn) = n . The components of v are real numbers, which is the reason for the letter r In mathematics, the dimension of a vector space v is the cardinality (i.e., the number of vectors) of a basis of v over its base field
[1][2] it is sometimes called hamel dimension (after georg hamel) or algebraic dimension to distinguish it from other types of dimension.
In r programming language, a vector has no dimension property and is just a sequence with its elements being of the same type 如果一个向量空间能够由某个有限长度的向量组张成得来，那么称该向量空间是 有限维的 (finite-dimensional)，否则称是 无限维的 (infinite-dimensional) ． Each space rn consists of a whole collection of vectors R5 contains all column vectors with five components
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