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Find out if nxn matrix is diagonalisable based on det(XI-A)

  1. May 25, 2009 #1
    1. The problem statement, all variables and given/known data

    If you need to check whether an nxn matrix, A, is diagonalisable or not, do you just find out what det(XI-A) is, and then if X has n distinct values it is diagonalisable, otherwise it's not.



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 25, 2009 #2

    matt grime

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    Re: diagonalisable?

    Consider the identity matrix...
     
  4. May 25, 2009 #3
    Re: diagonalisable?

    The identity matrix has only one distinct solution, 1, but it is diagonalisable...

    So how do you go about checking whether or not a matrix is diagonalisable or not?
     
  5. May 25, 2009 #4
    Re: diagonalisable?

    A nxn square matrix is diagonizable if it has n linearly independent eigenvectors. Having n distinct eigenvalues is sufficient but not necessary for diagonalizability.
     
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