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Linear Operators, Eigenvalues

  1. Oct 29, 2006 #1
    If A & B are linear operators, and AY=aY & BY=bY, what is the relationship between A & B such that e^A*e^B=e^(A+B)?? --where e^x=1+x+x^2/2+x^3/3!+...+x^n/n!
     
    Last edited: Oct 29, 2006
  2. jcsd
  3. Oct 29, 2006 #2

    StatusX

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    e^A e^B = e^(A+B) is true when A and B commute (AB=BA). Or are you asking when e^A e^B Y=e^(A+B) Y, where Y is an eigenvector of A and B? That is always true.
     
    Last edited: Oct 29, 2006
  4. Oct 29, 2006 #3

    mathman

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    A and B commute is sufficient - I don't know if it's necessary.
     
  5. Oct 29, 2006 #4

    Office_Shredder

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    I'm not quite sure what the question is asking here....

    I definitely did pick up that A and B must be the same size for A+B to exist (and must be square to have eigenvectors and values). Also, you need AB=BA (I think?). Someone else should verify this
     
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