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

If A is a 6x6 matrix with characteristic polynomial:

x^2(x-1)(x-2)^3

what are the possible dimensions of the eigenspaces?

3. The attempt at a solution

The solution given is that, for each each eigenspace, the smallest possible dimension is 1 and the largest is the multiplicity of the eigenvalue (the number of times the root of the characteristic polynomial is repeated). So, for the eigenspace corresponding to the eigenvalue 2, the dimension is 1, 2, or 3.

I do not understand where this answer comes from. Please come someone help me understand this.

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

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!

# Homework Help: Possible dimensions of eigenspaces, known characteristic polynomial

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