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Considering the 3x3 matrix:

m = {{0, -(I/Sqrt[2]), 0}, {I/Sqrt[2], 0, -(I/Sqrt[2])}, {0, I/Sqrt[2], 0}}

How would I find its normalized vectors eigenvectors u_i and construct the matrix U with column vectors u_i? I tried using Noralize[Eigeinvectors[m]] but it threw an error so I don't know what to do now.

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    $\begingroup$ Try Normalize /@ Eigenvectors[m] instead. To get the matrix where the columns are the normalized eigenvectors, do Normalize /@ Eigenvectors[m] // Transpose. $\endgroup$ – march Apr 15 '16 at 5:27
  • $\begingroup$ Eigenvectors@N@m also gives normalized eigenvectors, but they are numeric of course $\endgroup$ – Jason B. Apr 15 '16 at 7:17

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