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Homework Help: Why does x-axis have eigenvalue = 1

  1. Mar 4, 2006 #1
    Why has the x axis have an eigenvalue = 1 and the y axis an eigenvalue =-1? (please stay simple in your answers)
     
  2. jcsd
  3. Mar 4, 2006 #2

    LeonhardEuler

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    Could you be more specific? An eigenvalue as I understand it is generally associated with a function and a vector. I don't understand what the function is here.
     
  4. Mar 4, 2006 #3
    Our lecturer, just drew a diagram the other day on the board with an arrow pointing to the x-axis with lambda = 1 and another arrow with lambda = -1 pointing to the y-axis? Does anyone get what he was trying to explain? Many thanks
     
  5. Mar 4, 2006 #4

    LeonhardEuler

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    Maybe he was talking about the eigenvalues of some particular function which had the unit vectors in the x- and y-directions as eigenvectors. For example, the function f([x,y])=[x,-y] has the unit vectors [1,0] and [0,1] as eigenvectors with these eigenvalues because f([1,0])=[1,0]=1*[1,0] and f([0,1])=[0,-1]=-1*[0,1]. Or maybe he was talking about something entirely different. It's hard to say since I don't know what subject he was discussing.
     
  6. Mar 4, 2006 #5
    I think that was it. Thanks :-)
     
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