545 views
Let \(A(t)\) be a family of invertible real matrices depending on the real parameter \(t\) and assume they are invertible. Show that the inverse matrix \(A^{-1}(t)\) is invertible and give a formula for the derivative of \(A^{-1}(t)\) in terms of \(A^{\prime}(t)\) and \(A^{-1}(t)\). Thus one needs to investigate
\[
\lim _{h \rightarrow 0} \frac{A^{-1}(t+h)-A^{-1}(t)}{h}
\]
55% Accept Rate Accepted 8191 answers out of 14789 questions

Please log in or register to answer this question.

This site uses cookies to provide quality services and to analyze traffic. For more information, see the Privacy Policy