- #1
Demon117
- 165
- 1
Homework Statement
If A, B are elements of Mat(n, R) and A is invertible, compute
[tex]\frac{d}{dt}_{t=0}(A+tB)^{-1}[/tex]
The Attempt at a Solution
The derivative will be of the form
[tex]\frac{d}{dt}(A+tB)^{-1}=-(A+tB)^{-1}\frac{d}{dt}((A+tB))(A+tB)^{-1}[/tex]
but I need to evaluate this at t=0, so how do I simplify the expression on the right hand side? Since d/dt is a linear operator do I just attack each term individually, that is, take a derivative of A with respect to t plus a derivative of tB with respect to t?
This really is hard notation for me to follow.