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)
The Beginning Of All Things To End.
The End Of All Things To Come.
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.