A vector space is a set endowed with a rules for addition, and scalar multiplication. They must obey the following. For elements in the set f, g, and/or h.

1.(f+g)+h=f+(g+h) and c(kf)=(ck)f

This rule means that all elements in a vector space must obey the rules of association using both addition and multiplication.

2.f+g=g+f

This rule means that all elements in a vector space must obey the rules of commutation.

3.There exists one neutral element n in V such that f+n=f, which also denotes that n = 0.

4.There exists an element g in V such that f+g = 0. This denotes that for every element f there exists an element g which is equal to -f.

5.k(f+g)=kf+kg and (c+k)f=cf+kf

This rule means that all elements in a vector space must obey the rules of distribution.

6.1f=f

This ensures that a vector space obeys identity operations.

## No comments:

## Post a Comment