My Math Forum exponential map of matrix

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 June 8th, 2012, 06:22 AM #1 Newbie   Joined: Jun 2012 Posts: 3 Thanks: 0 exponential map of matrix I don't understand why the exponential map of matrix is a continous mapping of Mn(C) into itself. I need an exact proof! Thanks
 June 9th, 2012, 03:35 AM #2 Member   Joined: Jul 2011 From: Trieste but ever Naples in my heart! Italy, UE. Posts: 62 Thanks: 0 You can strat to prove that every matrix in $M_n(\mathbb{C})$ define a continuous function into itself! P.S.: I hope that I have write right.
 June 10th, 2012, 01:23 AM #3 Member     Joined: Mar 2011 Posts: 49 Thanks: 5 Re: exponential map of matrix Hint: You can use : $||e^{A+H} - e^A|| \leq ||H|| e^{||H||} e^{||A||}$ forall matrix $A$ and $H$

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