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 April 28th, 2016, 05:21 PM #1 Newbie   Joined: Apr 2016 From: Japan Posts: 2 Thanks: 0 A formula using det & tr I've found a formula on one of my notebooks. $\displaystyle \frac{d}{dt} \det X(t) = \det X(t) \tr( X^{-1}(t) \frac{d}{dt} X(t) )$ Does anyone knoe how to prove it? June 3rd, 2016, 04:58 PM #2 Member   Joined: May 2013 Posts: 31 Thanks: 3 This formula can be obtained from the Jacobi formula. An attempt would to use: 1) Jacobi's formula for express the derivative of the determinant of A in terms of the adjugate of A and the derivative of A: $\displaystyle \frac{d}{dt} \det A(t) = \mathrm{tr} \left (\mathrm{adj}(A(t)) \, \frac{dA(t)}{dt}\right )$ 2) Assuming that A is invertible, is true: $\displaystyle A^{-1} = \det A^{-1} adj A.$ See: https://en.wikipedia.org/wiki/Jacobi's_formula June 3rd, 2016, 09:48 PM #3 Newbie   Joined: Apr 2016 From: Japan Posts: 2 Thanks: 0 Now I can understand well. Thank you very much,Prokhartchin! Tags det, formula Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post db561 Math 2 February 29th, 2016 03:00 PM NuNu_dagobah Computer Science 4 January 8th, 2013 07:31 AM smchugh1982 Computer Science 1 October 7th, 2009 10:10 AM smchugh1982 Complex Analysis 0 October 7th, 2009 06:20 AM agro Probability and Statistics 3 August 27th, 2009 06:17 AM

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