1. The problem statement, all variables and given/known data This is my first post, so forgive me if anything's out of order. Assumean operator A satisfies the following equation: 1+2A-A^2-2A^3=0 Find the eigenvalues and eigenvectors for A 2. Relevant equations 3. The attempt at a solution So the eigenvalues are +1,-1, and -1/2. At least those are the values which satisfy the characteristic equation above. What I don't know is how to find the associated eigenvectors (without being given a concrete matrix). Is there a better way to solve this than making up a general 3x3 matrix and muddling through the (A-λI)v=λv equations? Thanks.