Eigenvectors and Eigenvalues of a Linear Map
Suppose I had a linear map such that and I want to find the eigenvalues and eigenvectors of T.
I'm doing this without determinants. I have it that
After rearranging terms and doing simple elimination I have
I believe the eigenvalue is then . Next to find the eigenvectors I would find
To find I would end up having that
and so I have . I believe this means that all eigenvectors would be in the form (i.e. (1,1),(2,2)...)
Was everything I did correct?