1

I want to find the derivative of $$x=\exp{At}$$ with respect to $A$. In this case $A$ is a matrix. Is the solution $$\frac{\mathrm dx}{\mathrm dA}=t\cdot \exp{At}$$ Or is it different?

AlexR
  • 24,905
darwin rajpal
  • 363
  • 1
    I suspect this is only true when $A$ commutes with all matrices, because then $\exp((A+H)t)=\exp(A)(I_n+tH+O(H^2))$. If this is not the case, $\exp((A+H)t)=\exp(tA)+tH+t^2/2(AH+HA)+t^3/6(A^2H+AHA+HA^2)+\cdots +O(H^2)$. – zuggg May 19 '15 at 12:25
  • What do you mean by ${d\over dA}$ when $A$ is a matrix variable? – Christian Blatter May 19 '15 at 12:37

0 Answers0