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How to determine which eigenvalue has multiplicity 2 ?

  1. May 20, 2012 #1
    Say I have a 4x4 matrix and I know 3 eigenvalues and the 3 corresponding eigenvectors.

    Is there a fast way to calculate which one has multiplicity 2 without calculating the characteristic polynomial(too time consuming for a 4x4 matrix) or without determining the dimensions of (A-λ I) for each eigenvalue λ. (Row reducing 3 4x4 matrices is too long during an exam)
     
  2. jcsd
  3. May 20, 2012 #2
    LOL i just though of the solution as soon as I typed the question.

    I guess I could set up an equation using the definition of trace:

    Ʃ(elements of diagnal)=λ1+λ2+λ3+x

    hence work out x, which will tell me which eigenvalue is repeated.
     
  4. May 20, 2012 #3

    tiny-tim

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    nice! :smile:
     
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