1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Eigenvector proof

  1. Aug 12, 2014 #1
    Hello PF, brand new member here.

    A question about a proof:

    If A*v=λ*v, then w = c*v is also an eigenvector of A.

    This seems really simple to me, but perhaps I am doing it incorrectly:

    A*c*v=λ*c*v, divide both sides by c and you are left with your original eigenvector of A. Am I missing something here?
  2. jcsd
  3. Aug 12, 2014 #2
    What you've shown is that if cv is an eigenvector, then v is an eigenvector. You need to show the other way. In addition, you can't always divide by c.

    Also, this should be in homework help.
  4. Aug 13, 2014 #3


    User Avatar
    Science Advisor
    Gold Member

    notice that subspaces are closed under scaling. Or just factor out the c as the matrix cId.
  5. Aug 13, 2014 #4


    User Avatar
    Homework Helper

    Welcome to PF!:smile:
    Do not use * when applying an operator on a vector. The operator A assigns a vector u to vector v. Write u=A(v). In case v is an eigenvector of operator A, A(v)= λ*v. The right side is a product - a vector multiplied by a scalar, but the left-hand side is not.

    You can use the property of linear operators that A(cv)=c A(v) (c is a scalar).

    Last edited: Aug 13, 2014
  6. Aug 13, 2014 #5


    User Avatar
    Science Advisor

    As you have been told, what you shown is that "If cv is an eigenvector of A with eigenvalue λ then so is v". To prove the other way, reverse your proof: from Av= λv, multiply both sides by c.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted