(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hi, I'm going over an old exam paper as part of my revision for upcoming exams (joy !! ok, maybe not :yuck: )

Anyway, I've gotten myself a bit lost here and would appreciate some guidance.

Here we go:

Compute the eigenvalues & eigenvectors of the following matrix. Normalise the 2 eigenvectors.

Matrix = (3 1+i)

(1-i 2)

2. Relevant equations

3. The attempt at a solution

So far I have the 2 eigenvalues being +1 and +4, but I'm having trouble with the next bit, I think that the eigenvectors will come out as complex numbers,

so far I have reduced to two equations:

2x + (1+i)y = 0

(1-i)x + y = 0

ie 2x + (y+iy) = 0 (so, 2x = -y-iy)

and x-ix + y = 0 (and y = -x+ix)

Is this correct?? if not why? and where do I go from here?

Also, I don't get the idea of normalisation (next part of question), I understand that it has something to do with setting the vector(i think) to 1, but I'm not sure. My lecturers notes aren't the easiest to follow outside of his lectures, so if you could walk me through it a bit I'd be very grateful.

Thanks

Kel

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Eigenvectors & normalising

**Physics Forums | Science Articles, Homework Help, Discussion**