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Find the Eigenvalue Problem

  1. Mar 3, 2014 #1
    1. The problem statement, all variables and given/known data

    Let there be a 4X4 Matrix A with dim(im(A), or rank = 1 , and trace=10. What are the Eigenvalues of A? Are there any multiplicities?

    3. The attempt at a solution

    While I understand that the trace of a matrix that's 4X4 = the sum of the diagonal elements, I'm confused about how to create this matrix A to find the eigenvalues, and how to represent the given fact that dim(im(A)) = 1.

    Any tips/pointers would be helpful!
     
  2. jcsd
  3. Mar 3, 2014 #2

    Simon Bridge

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    You need to review what is meant by the image and dimension of a matrix: what does rank=1 tell you?
    Also - do you know of any special cases where the eigenvalues have some simple relation to the trace?
    https://www.physicsforums.com/showthread.php?t=682216

    Since it is 4x4 - you can always just assign 16 variables and sketch it out.
    Needs lots of paper or a large whiteboard (or window).
     
    Last edited: Mar 3, 2014
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