Could someone describe the eigenvalues of $ \left( \begin{array}{cc} 2 & 1 \\ -1 & 2 \end{array} \right) $, as well as the bases of the corresponding eigenspaces?
I received eigenvalues of $ \lambda = 2+i, 2-i$. And $ E_{2+i} = \operatorname{span}\{[1,i]^T\}$ and $E_{2-i} = \operatorname{span}\{ [1,-i]^T\}$. It also wants me to illustrate the action of $A$ on eigenvectors. How would I do so?
Are these solutions correct?
You are correct except the eigenvectors are $$ E_{2+i} = (1,i)^t\\ E_{2-i} = (1,-i)^t $$
The action of $A$ on eigenvalue $E_\lambda$ is to multiply it by $\lambda$