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Normalized Eigenvector

Posted 10 years ago
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I have the matrix A = {{7, 0, 0}, {0, 1, -I}, {0, I, -1}} which I got out of a book. I get the eigenvalues a1=7, a2= Sqrt[2], a3= -Sqrt[2] with Mathematica just as the book example.
How can I use Mathematica to acquire the normalized eigenvectors (column matrices), as in the book example
|a1> = (1, 0, 0), |a2> = (0, 1/Sqrt[2(2-Sqrt[2])], I(Sqrt[2]-1)/Sqrt[2(2-Sqrt[2])]
|a3> = (0, 1/Sqrt[2(2+Sqrt[2])], -I(1+Sqrt[2]/Sqrt[2(2+Sqrt[2])]

Thank you in advance.
POSTED BY: sean roubion
Simplify[Normalize /@ Eigenvectors[A]]
(Of course, these are unique only up to multplication with a scalar with absolute value 1)
POSTED BY: Ilian Gachevski
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