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#1 2007-09-10 08:14:28

Registered: 2006-05-05
Posts: 1,470

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 (2007-09-10 08:17:16)

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#2 2013-09-26 19:58:25

From: Bumpkinland
Registered: 2009-04-12
Posts: 102,328

Re: finding eigen values in 3x3 symmetrical matrix


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.
If it ain't broke, fix it until it is.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.


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