While preparing for a test, I was faced with the following task: Find the eigenvalues and eigenvectors of a linear transformation $\phi$ specified by a matrix:
$$ A = (a_1, a_2,\ldots, a_n)^T(b_1, b_2,\ldots, b_n) \neq 0 $$
And also find a necessary and sufficient condition for its diagonalizability.
I understand how to find the eigenvalues and eigenvectors of a linear transformation in a special case, but I don’t understand how to do it in such a general case. I would really appreciate any help!