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Diagonalization of square matrix if not all eigenvalues are distinct of

  1. Sep 7, 2011 #1
    Is it possible to diagonalize such matrix? and how would one do it?
     
  2. jcsd
  3. Sep 7, 2011 #2

    micromass

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    Yes, it is possible to diagonalize such a matrix. One has to find the eigenspaces and a basis for the eigenspaces. Take all the basisvectors for the eigenspaces, if they span the entire space, then the matrix is diagonalizable.
    Taking all the basis eigenvectors as a basis gives you the required diagonal matrix.
     
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