       Re: orthonormal eigenvectors

• To: mathgroup at smc.vnet.net
• Subject: [mg88415] Re: orthonormal eigenvectors
• From: Bill Rowe <readnews at sbcglobal.net>
• Date: Mon, 5 May 2008 06:10:40 -0400 (EDT)

```On 5/3/08 at 6:18 AM, nairbdm at hotmail.com (. .) 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.

You can find a set of eigenvectors by doing:

In:= m = {{1, -I (2^(1/2)), 0},
{I (2^(1/2)), 0, 0},
{0, 0, 2}};

In:= ev = Eigenvectors[m]

Out= {{0, 0, 1}, {-I Sqrt, 1, 0}, {I/Sqrt, 1, 0}}

Then it is easy to normalize these by doing:

In:= len = (#.#) & /@ ev;
ev /Sqrt[len]

Out= {{0, 0, 1}, {-Sqrt, -I, 0}, {I, Sqrt, 0}}

But while all of these have unit length, they do not form an
orthonormal set since

In:= Dot @@ Rest[%]

Out= -2 I Sqrt

which is clearly not zero. That is for your matrix, a set of
orthonormal eigenvectors doesn't exist.

```

• Prev by Date: Re: StringMatchQ and Regular Expressions
• Next by Date: Re: Fit data with range
• Previous by thread: Re: orthonormal eigenvectors
• Next by thread: Re: orthonormal eigenvectors