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Multiple eigenvalues - any hints would be appreciated

  1. Nov 26, 2011 #1
    1. The problem statement, all variables and given/known data

    I need to prove that a 4x4 matrix has 2 zero eignenvalues.

    2. The attempt at a solution

    I have tried to obtain the characteristic equation but calculating the determinant of a relevant 4x4 is rather daunting as there aren't many zeros.

    I was wondering if there is any other way to prove the statement without resorting to this brute force approach.

    Thank you in advance!
  2. jcsd
  3. Nov 26, 2011 #2


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    Science Advisor

    I assume you mean that you have a specific 4 by 4 matrix that you have not shown us. No, there is no 'simple' way to calculate eigenvalues except for special matrices. Whether or not there exist a special trick for your matrix, we cannot say because you do not show us the matrix. Just calculate the determinant of [itex]A- \lambda I[/itex] and set it equal to 0. With a f4 by 4 matrix that will give you a fourth degree polynomial equation.
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