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Making a eigenvector a linear combination of other eigenvectors

  • Thread starter JordanGo
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  • #1
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Homework Statement


Write the eigenvector of [itex]\sigma[/itex]x with +1 eigenvalue as a linear combination of the eigenvectors of M.


Homework Equations



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

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)?
 

Answers and Replies

  • #2
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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.
 
  • #3
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Ok, that makes sense, thanks a lot!
 
  • #4
HallsofIvy
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Homework Statement


Write the eigenvector of [itex]\sigma[/itex]x with +1 eigenvalue as a linear combination of the eigenvectors of M.


Homework Equations



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

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)?
 

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