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Re: orthonormal eigenvectors

  • To: mathgroup at smc.vnet.net
  • Subject: [mg88403] Re: orthonormal eigenvectors
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Mon, 5 May 2008 06:08:30 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <fvhe57$400$1@smc.vnet.net>

. . wrote:

> I have a 3X3 matrix M:
> {1,-i(2^(1/2)),0}
> {i(2^(1/2)),0,0}
> {0,0,2}
> 
> And I am trying to find a set of orthonormal eigenvectors for M.
> If anyone can help, I would greatly appreciate it.

You could start by writing your matrix in correct Mathematica syntax, 
then read about (in the documentation center for instance) and use 
functions such as *Eigenvectors[]* or *Orthogonalize[]*.

m = {{1, (-i)*2^(1/2), 0}, {i*2^(1/2), 0, 0}, {0, 0, 2}};

Eigenvectors[m]

{{0, 0, 1}, {-((-1 + Sqrt[1 - 8 i^2])/(2 Sqrt[2] i)), 1,
   0}, {(1 + Sqrt[1 - 8 i^2])/(2 Sqrt[2] i), 1, 0}}

-- 
Jean-Marc


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