       Re: orthonormal eigenvectors

• To: mathgroup at smc.vnet.net
• Subject: [mg88447] Re: orthonormal eigenvectors
• From: tommcd <TCMcDermott at gmail.com>
• Date: Mon, 5 May 2008 06:16:27 -0400 (EDT)
• References: <fvhe57\$400\$1@smc.vnet.net>

```On May 3, 11:18 am, ". ." <nair... at hotmail.com> wrote:
> Dear MathGroup,
>
> 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.
>
> Thanks,
> Brian

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

Eigenvectors[m]
{{0, 0, 1}, {-I Sqrt, 1, 0}, {I/Sqrt, 1, 0}}

Eigenvalues[m]
{2, 2, -1}

Orthogonalize[m]
{{1/Sqrt, -I Sqrt[2/3], 0}, {I Sqrt[2/3], -(1/Sqrt),
0}, {0, 0, 1}}

```

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