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