Is it possible to find a matrix $A$ given an arbitrary matrix exponential $e^{tA}$?
It seems to me that this is definitely possible if $A$ has distinct eigenvalues. This is because
$$ e^{tA} = v_1 e^{t \lambda_1 } c_1 + v_2 e^{t \lambda_2 } c_2 + \;...\; + v_n e^{n \lambda_n } c_n $$ for an $n$ x $n$ matrix $A$. So given $e^{tA}$ we are indirectly given the eigenvalues and eigenvectors.
Is this possible to do if $A$ has repeated eigenvalues?
