Injective and surjective?

  • Thread starter ylem
  • Start date
  • #1
32
1
Hello! I hope I've posted this in the correct section...

I'm a 3rd year undergraduate and we're currently studying Vector Spaces (in QM) and I just don't understand what injective (one-to-one) and surjective (onto) mean? As a result I have no idea what an isomorphism is!

I realise this is probably a very simple question, but I'm just struggling so much with the course!

Cheers, Samantha
 

Answers and Replies

  • #2
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
10,025
134
Ok, the first thing you have two focus on, is that you have two SETS, call them A and B.
Both A and B has elements, determinable by some criterion.


Now, a MAPPING from A to B takes each element in A and "relates" it to some unique element in B.

To say that a mapping is injective means that there are no two elements in A that are related to the same element in B. Thus, knowing the mapping procedure along with the element in B, we can DEDUCE from this what is the element in A which is related to the known element in A.
If we denote the element in B related to element x in A with f(x), this means that if f(x)=f(y), then x=y (only ONE unique element in A is related to the value of f(x))

To say that a map is SURJECTIVE means that whatever element Y in B you pick out, there exist an x in A so that Y=f(x).
The map covers B, so to speak.

Is this clear?
 
  • #3
32
1
Yeah! Thanks a lot :-)
 

Related Threads on Injective and surjective?

Replies
0
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
2
Views
2K
Replies
4
Views
2K
Replies
11
Views
5K
Replies
2
Views
652
Replies
9
Views
1K
Replies
2
Views
3K
Top