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  •  » finding eigen values in 3x3 symmetrical matrix

#1 2007-09-11 06:14:28

luca-deltodesco
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finding eigen values in 3x3 symmetrical matrix

how can i go about calculating the eigen values of a 3x3 symmetrical matrix for example:



if i do:



i end up getting a cubic equation in terms of the eigen value which i don't know how to solve, and im sure there must be a simpler way, if not calculating them, atleast showing that they are more or less than 0

Last edited by luca-deltodesco (2007-09-11 06:17:16)


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#2 2013-09-27 17:58:25

bobbym
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Re: finding eigen values in 3x3 symmetrical matrix

Hi;

atleast showing that they are more or less than 0

An oldie but a goodie.

You get the characteristic polynomial



You can solve for the roots numerically or by graphing but a more precise idea is to use a Sturm chain.









Substitute the endpoints of 0 and infinity.



Count the sign changes. We get 3.

So we get there are 3 roots between 0 and infinity and since 0 is not a root all 3 are greater than 0.

A numerical attack yields:



for the three roots.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.
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