Re: orthonormal eigenvectors
- To: mathgroup at smc.vnet.net
- Subject: [mg67621] Re: [mg67576] orthonormal eigenvectors
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Sun, 2 Jul 2006 06:28:06 -0400 (EDT)
- References: <200607010912.FAA20405@smc.vnet.net> <024C3AAB-F15C-41D1-8357-BF61A00C9252@mimuw.edu.pl> <Pine.LNX.4.58.0607020937060.4262@mp.okayama-u.ac.jp>
- Sender: owner-wri-mathgroup at wolfram.com
But this example is no good, since this matrix is not symmetric (real
hermitian). A real symmetric matrix can be diagonalized by an
orthognonal matrix. This is not true for arbitrary real matrics.
Andrzej Kozlowski
On 2 Jul 2006, at 09:48, tkghosh wrote:
>
>
> Thanks for your reply and sorry for not giving an example.
>
> I am giving here a simple example of 6 X 6 matrix, although the
> actual matrix is 11 X 11 matrix.
>
> Suppose 6 X 6 matrix is the following:
>
> M = {{306.25, -306.25, 0, 0, 0, 0},{-102.083, 310.25, -204.167, 0,
> 0, 0},
> {0, -122.5, 318.25, -183.75, 0, 0}, {0, 0, -131.25, 330.25,
> -175.,0},
> {0, 0, 0, -136.111, 346.25, -170.139}, {0, 0, 0, 0, -139.205,
> 366.25}}
>
>
>
> {w, v} = Eigensystem[M]; (* "w" is the Eigenvalues and "v"
> Eigenvectors *)
>
> v[[6]].v[[5]] = -0.57199
>
> v[[6]].v[[3]] = 0.327911
>
> v[[6]].v[[1]] = -0.15311
>
> It cleary shows that the vectors are not orthogonal.
> However, these vectors are normalized.
> You are correct that the matirx M has a pecuiliar shape and
> I must use some other subtle method to compute them. Do not
> know what method is most suitable.
>
> Do you have any idea how to solve that kind of matrix (M) and
> how to get an orthogonal vectors?
>
> Any help is welcome.
>
> Thanking you again.
> Tarun
- References:
- orthonormal eigenvectors
- From: tkg <tkghosh@mp.okayama-u.ac.jp>
- orthonormal eigenvectors