Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook