Prove that if $y'(t)=A(t)y(t)$ and $\psi(t)=e^{At}$ then $\eta(t)$ is the fudamental matrix of the adjoint system iff $\psi^*\eta$ is a constant invertible matrix.
$A^*(t)$ is the conjugate transpose of the $n\times n$ matrix $A(t)$
It is given $x(t)=-A^*(t)y(t)$ is the adjoint system, but in that case I think we can prove $\psi^*\eta=I$. What really is meant by adjoint system of equations ?
And how do I prove it ?