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 Post subject: Finding eigenvectors of an unusual matrixPosted: Sat, 15 Jan 2011 10:55:09 UTC
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Joined: Sat, 15 Jan 2011 10:36:31 UTC
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Hello, I'm trying to find the eigenvector(s) of the following matrix:

I already know that it's a doubled eigenvalue of , obvious given that it's a diagonal matrix. However, I'm having trouble finding the eigenvectors, because when solving:

You can't really do the system of equations because you just end up with:
.

Which just gives you

which isn't really anything you can use to solve for the eigenvector .

Could anyone tell me what the eigenvectors are, and more importantly, how they were found?

This is in the context of finding the general solution to the system

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 Post subject: Re: Finding eigenvectors of an unusual matrixPosted: Sat, 15 Jan 2011 13:19:43 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
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shallarock wrote:
Hello, I'm trying to find the eigenvector(s) of the following matrix:

I already know that it's a doubled eigenvalue of , obvious given that it's a diagonal matrix. However, I'm having trouble finding the eigenvectors, because when solving:

You can't really do the system of equations because you just end up with:
.

Which just gives you

which isn't really anything you can use to solve for the eigenvector .

Could anyone tell me what the eigenvectors are, and more importantly, how they were found?

This is in the context of finding the general solution to the system

It is not a diagonal matrix, and it is not diagonalisable either.

The dimension of the 2-eigenspace is only 1. You should see immediately from your system of equations that .

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