Re: Eigenvalue and eigenvectors of a 10x10 matrix

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• Subject: [mg128086] Re: Eigenvalue and eigenvectors of a 10x10 matrix
• From: Ray Koopman <koopman at sfu.ca>
• Date: Fri, 14 Sep 2012 00:25:15 -0400 (EDT)
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On Sep 13, 12:43 am, Redeemed <cakp... at gmail.com> wrote:
> I want to do the eigen analysis of the matrix below
> mat := {{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {-(1 + K + K1), -0.1, K, 0, 0,
>      0, 0, 0, K1, 0},
>    {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {K, 0, -(1 + 2 K + K1), -0.1, K, 0,
>      0, 0, K1, 0},
>    {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, K, 0, -(1 + 2 K + K1), -0.1,
>      K, 0, K1, 0},
>    {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, K,
>     0, -(1 + K + K1), -0.1, K1, 0},
>    {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {K1, 0, K1, 0, K1, 0, K1,
>     0, -(1 + 4 K1), -0.1}};
>
> I kept getting a long solution with some Root [] and #1
> I do not know what I am doing wrong
> Any help,
> Its very urgent
>
> Thanks

Change .1 to 1/10

mat = {
{0, 1, 0, 0, 0, 0, 0, 0, 0, 0},
{-(1+K+K1), -1/10, K, 0, 0, 0, 0, 0, K1, 0},
{0, 0, 0, 1, 0, 0, 0, 0, 0, 0},
{K, 0, -(1+2K+K1), -1/10, K, 0, 0, 0, K1, 0},
{0, 0, 0, 0, 0, 1, 0, 0, 0, 0},
{0, 0, K, 0, -(1+2K+K1), -1/10, K, 0, K1, 0},
{0, 0, 0, 0, 0, 0, 0, 1, 0, 0},
{0, 0, 0, 0, K, 0, -(1+K+K1), -1/10, K1, 0},
{0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{K1, 0, K1, 0, K1, 0, K1, 0, -(1+4K1), -1/10}};

Eigenvalues[mat]

{(1/20)*(-1 + I*Sqrt[399]),
(1/20)*(-1 - I*Sqrt[399]),
(1/20)*(-1 - Sqrt[-399 - 2000*K1]),
(1/20)*(-1 + Sqrt[-399 - 2000*K1]),
(1/20)*(-1 - Sqrt[-399 - 800*K - 400*K1]),
(1/20)*(-1 + Sqrt[-399 - 800*K - 400*K1]),
(1/20)*(-1 - Sqrt[-399 - 800*K - 400*Sqrt[2]*K - 400*K1]),
(1/20)*(-1 + Sqrt[-399 - 800*K - 400*Sqrt[2]*K - 400*K1]),
(1/20)*(-1 - Sqrt[-399 - 800*K + 400*Sqrt[2]*K - 400*K1]),
(1/20)*(-1 + Sqrt[-399 - 800*K + 400*Sqrt[2]*K - 400*K1])}

Eigensystem[mat]  returns similar output, but too much to give here.

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