Algebra Question (Maths!)

titaniumx3 · 4 Dec 2006 at 18:27

I would really appreciate some input on this question as I've been scratching my head all day and still can't figure it out!

The question is:

Let A be a 2x2 matrix over C. If both the eigenvalues of A are 0, then must A be the zero matrix? Explain

Any ideas?

DaveF · 4 Dec 2006 at 18:34

I don't want to just give you an answer, but the matrix A doesn't need to be zero. You might want to have a look at "Jordan Normal Forms".

Arcade Fire · 4 Dec 2006 at 18:41

What he said. Or have a think about the eigenvalues of an upper triangular matrix.

Tokenbrit · 4 Dec 2006 at 18:42

Solve |A-lambda*I| = 0 for the general matrix A over C to get you started.

titaniumx3 · 4 Dec 2006 at 18:47

DaveF said:
I don't want to just give you an answer, but the matrix A doesn't need to be zero. You might want to have a look at "Jordan Normal Forms".

Thanks for the reply. We haven't actually covered this in lectures yet, but I'm going to read up on it anyway and see if it will help. I'm guessing the actual explanation is a lot more basic though.

titaniumx3 · 4 Dec 2006 at 19:08

Damn, come to think of it the answer is pretty obvious. I was thinking it would be some special property of the complex numbers. The embarrasment is killing me now!