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,
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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