Unique identity and inverse question.

  • Thread starter loli12
  • Start date
  • #1
When we say that the identity and inverse element in a vector space is unique, does it mean that those elements are the same for all x in V? or does it mean that each x has its own unique identity or inverse element?

moreover, is there a geometric way of explaning what a field is? because I got confused about the scalar multiplication of a vector space that b in F and c in V which give bc in V..

and also, did anyone used Linear Algebra by Friedberg, Insel and Spense before? What do you think about the book?
 

Answers and Replies

  • #2
fourier jr
757
13
unique identity means the whole algebraic system (group, ring or field, etc) has exactly one element e with the property that ae = ea = a for EVERY a in the object you're interested in. same goes for 'unique inverse' & so on.
 

Suggested for: Unique identity and inverse question.

  • Last Post
Replies
2
Views
546
  • Last Post
Replies
24
Views
653
Replies
34
Views
760
  • Last Post
Replies
5
Views
529
  • Last Post
Replies
2
Views
526
Replies
2
Views
783
  • Last Post
Replies
6
Views
449
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
13
Views
2K
  • Last Post
Replies
3
Views
701
Top