# How to find eigenvalues and eigenvectors for 5x5 matrix

1. Dec 8, 2011

### DavidLiew

I got a 5x5 matrix, if use characteristic equation to find the eigenvalues and eigenvectors are very tedious and trouble, so got any method which are easy to calculate?

2. Dec 8, 2011

### genericusrnme

unless you've got a nice matrix (read diagonal) you're going to have to use some tricks, if you're lucky you can use the tschirnhaus transformation but most likely you'll have to resort to numerical approximations for the eigenvalues (newtons method or something) then you'll have to churn through to find the nullspace manually

it's pretty tedious work and chances are that you'd end up making an error doing it anyway..
you could just use mathematica or matlab, that'd be easier

if you don't have any of those, post your matrix and I'll give you the results, if you want?

3. Dec 8, 2011

### DavidLiew

I need to do it in paper, can not use software to solve.

4. Dec 8, 2011

### genericusrnme

in that case I'd say you're going to be stuck with inspection, newtons method or something like it or if you're lucky you may be able to reduce it to an easier polynomial via some transformation

sorry bro

5. Dec 8, 2011

### HallsofIvy

Staff Emeritus
If you are given exercises in which you are asked to find eigenvalues of 5 by 5 matrices by hand, I suspect it will have been set up so the characteristic equations have small integer roots. Once you have the polynomials, you might try the "rational root" theorem to narrow your choices.

6. Dec 8, 2011

### Ray Vickson

Instead of matlab or mathematica, he/she might prefer to use Maple.

RGV

7. Dec 8, 2011