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Eigenvalue vector x

  1. Dec 8, 2013 #1
    Question one: in regards to two segments underlined in blue.

    If (a,x) is an eigenvalue and vector of A, that means

    Ax = ax, where a is a real number.

    My question is, is Amx = amx, where m in an integer greater than 1?


    Question 2: in regards to two segments underlined in red.

    I know that I*x = x, where I is the nxn identity matrix and x is a vector in Rn.
    But the last part where the vector x is factored, shouldn't the 1 be an I?
     

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  3. Dec 8, 2013 #2

    Dick

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    Yes, ##A^mx=a^mx##. You should try to prove that if you aren't sure. For the second question what they factored out are scalars. Since Ix=1x what you factor out should be the scalar 1, not the matrix I.
     
  4. Dec 8, 2013 #3

    Ray Vickson

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    Note: do NOT assume that the eigenvalue is real: it may not be. Some matrices have only real eigenvalues, others have some that are complex.
     
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