“scalar multiplication”的概念、定义、习题解题方法及翻译-数学辞典

单词

scalar multiplication

释义

scalar multiplication

One of the two operations in a vector space V, together with addition. Given any vector v in V and scalar c (from the base field), the scalar multiple cv ε V may be formed. It may be that v = v is a coordinate vector, in which case the coordinates of cv are those of v multiplied by c. If v = A is a matrix, then the entries of cA are the entries of A multiplied by c. Multiplication by scalars has the following properties:

(i) (h+k)v = hv+kv.

(ii) k(v+w) = kv+kw.

(iii) h(kv) = (hk)v.

(iv) 1v = v.

Geometrically, if v is in Rn, then the scalar multiples cv comprise the line through v and the origin 0; when c > 0, the scalar mutliples comprise the half-line from 0 through v.

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数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。