多项式向量场空间的维数与基  

The Dimension and Base of Vector Fields Space of Polynomial

作　　者：冯光庭[1] 

机构地区：[1]湖北第二师范学院数学与计量经济系,武汉430205

出　　处：《湖北第二师范学院学报》2009年第2期10-11,共2页Journal of Hubei University of Education

摘　　要：本文借助于数域P上的n次多项式的齐次分解,证明了线性空间P[X1,X2,…Xn]m的维数等于Cnn+m并给出了该空间的一组基;进而得到Rn上次数不超过m的多项式向量场的全体构成的线性空间V的维数等于n.Cnn+m。By the means of the n - order moment polynomial of homogeneous decomposition on the domain, it is proved that P[X1,X2,…Xn]m,in the line space P of dimension is equal to Cn＋m^n and a set of base of the space is set up. A furthur conclustion is that the dimension of the linear space V constituted of the whole polynomial vector fields on R^n with degree equal to or less than m is equal to C·n＋m^n.

关 键 词：多项式 向量场 线性空间 维数 基 

分 类 号：O151.2[理学—数学]