suppose I have a symmetric matrix A in a differential equation,
$\displaystyle \frac{dx}{dt}+Ax=b$
Now, if $V=$ eigenspace of $A$ and $D=$ eigenvalue of $A$
we can write $x=V*c$, where $c=$ coefficients
then,
$\displaystyle \frac{d(V*c)}{dt}+A*(V*c)=b$
that is,
\displaystyle \frac{d(c)}{dt}+D*c=V'*b where V'*A*V=D
I think this procedure is very well known. But in my work, my prof is saying that if $A$ is unsymmetric, this procedure is still true. I am confused because my simulation showed it is not possible. I need help to know whether it is possible or not? please.