Ker(phi) = {0}, then phi injective?

  • Context: Undergrad 
  • Thread starter Thread starter ctrlaltdelete
  • Start date Start date
  • Tags Tags
    Injective Phi
ctrlaltdelete
Messages
1
Reaction score
0
Hi all,

Can anyone point to an explanation of why if ker(phi) = {0}, then phi is injective?
 
on Phys.org
Is "phi" a linear map?

Suppose that phi(x) = phi(y), and use some properties of linear maps to show that x = y.
 

Similar threads

MHB Kernel of Linear Map: Show $\ker \phi$ Equation
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad How do we distinguish two different notations for cokernel and coimage?
  • · Replies 41 ·
2
Replies
41
Views
5K
Undergrad Dfns group action & group, written in terms of the other
  • · Replies 26 ·
Replies
26
Views
2K
Undergrad Notation questions about kernel, cokernel, image and coimage
  • · Replies 7 ·
Replies
7
Views
2K
MHB Proving Equivalence of Statements Involving Endomorphisms - Can We Take $v=x$?
  • · Replies 10 ·
Replies
10
Views
3K
MHB Is $\Phi|_{U_2}$ a Vector Space Isomorphism?
  • · Replies 1 ·
Replies
1
Views
2K
MHB Is this a valid proof for the invertibility of $\Phi$?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Meaning of "identify" & variations in different math context
  • · Replies 5 ·
Replies
5
Views
2K
MHB Tensor Products - Dummit and Foote Section 10.4 Corollary 9
  • · Replies 37 ·
2
Replies
37
Views
7K
Undergrad Question about "A Group Epimorphism is Surjective"
  • · Replies 13 ·
Replies
13
Views
3K