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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

    HallsofIvy

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    Staff Emeritus
    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!

     
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