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: Making a eigenvector a linear combination of other eigenvectors

  1. Sep 27, 2012 #1
    1. The problem statement, all variables and given/known data
    Write the eigenvector of [itex]\sigma[/itex]x with +1 eigenvalue as a linear combination of the eigenvectors of M.

    2. Relevant equations

    [itex]\sigma[/itex]x = (0,1),(1,0) (these are the columns)

    3. The attempt at a solution

    .... Don't know what to do. Can someone show me how to do this using arbitrary eigenvectors, say (a,b) and (c,d)?
  2. jcsd
  3. Sep 28, 2012 #2
    Can you find the eigenvector in question? Let's denote it by (v,w). Then you can write
    (v,w) = C1(a,b) + C2(c,d) and solve the constant C's.
  4. Sep 28, 2012 #3
    Ok, that makes sense, thanks a lot!
  5. Sep 28, 2012 #4


    User Avatar
    Science Advisor

    Okay, that's [itex]\sigma[/itex]. What is M??? we can't write something "as a linear combination of the eigenvectors of M without knowing what M is!

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook