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

  • Context: Undergrad 
  • Thread starter Thread starter ctrlaltdelete
  • Start date Start date
  • Tags Tags
    Injective Phi
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
1 reply · 4K views
ctrlaltdelete
Messages
1
Reaction score
0
Hi all,

Can anyone point to an explanation of why if ker(phi) = {0}, then phi is injective?
 

Discussion

Physics news 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

Kernel of Linear Map: Show $\ker \phi$ Equation

  • mathmari
  • · Replies 5 ·
  • Linear and Abstract Algebra
Replies
5

Undergrad DimKer(T) = 0 <--> T is injective

  • Mr Davis 97
  • · Replies 6 ·
  • Linear and Abstract Algebra
Replies
6

Graduate Injective immersion and embedding

  • Korybut
  • · Replies 2 ·
  • Differential Geometry
Replies
2

High School How Can You Determine if an Operator is Surjective, Injective, or Bijective?

  • SeM
  • · Replies 7 ·
  • Linear and Abstract Algebra
Replies
7

Functions that are injective but not surjective

  • Math Amateur
  • · Replies 5 ·
  • Linear and Abstract Algebra
Replies
5

Undergrad Does this theorem need that Ker{F}=0?

  • jamalkoiyess
  • · Replies 1 ·
  • Linear and Abstract Algebra
Replies
1

Undergrad Show that linear transformation is surjective but not injective

  • pearl0993
  • · Replies 3 ·
  • Linear and Abstract Algebra
Replies
3

Undergrad I'm trying to prove that a linear map is injective

  • catcherintherye
  • · Replies 1 ·
  • Linear and Abstract Algebra
Replies
1

How to Prove the Dimension of Ker $\phi^2$ in a Finite-Dimensional Vector Space?

  • Chris L T521
  • · Replies 1 ·
  • Math Problem of the Week
Replies
1

Undergrad Is Every Cofibration Injective?

  • Euge
  • · Replies 1 ·
  • Math Problem of the Week
Replies
1