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