When to use eigenvector method

1. Feb 21, 2010

imaloonru

I'm a physics major. As such, I have come across several situations in my studies that require the use of eigenvectors and eigenvalues. Whenever I have to use this method, I've been told to. I do not have a complete understanding of eigenvectors and values and am wondering how you would spot a situation where you would need to use them.

For example, if I wanted to know when or where the rate of change of something was 0, I would take a derivative, set it equal to zero, then solve for some variable. What sort of situation would I look for (in general) that would make me say "Hey! I need to find some eigenvectors here."?

Thanks.

2. Feb 21, 2010

Redbelly98

Staff Emeritus
Welcome to PF.

In general, if you have an equation of the form
Matrix x Vector = Scalar x Vector​
or
Operator x Function = Scalar x Function​
The "Scalar" is an eigenvalue that you must find.

3. Feb 22, 2010

HallsofIvy

Also you can "simplify" linear transformations, writing them as matrices in either diagonal or Jordan normal form, with eigenvalues on the diagonal, by using the eigenvectors (or if there is not a complete set of eigenvectors, the "generalized" eigenvectors) as basis for the vector space.

4. Feb 22, 2010

imaloonru

Thanks guys. This helps.

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