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I have tried to think of a way to prove it, but neither my classmates or I found something. I looked up google etc, but all the proofs were with things that we didn't learn. Any help is welcome.

- Thread starter GregoryGr
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- #1

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I have tried to think of a way to prove it, but neither my classmates or I found something. I looked up google etc, but all the proofs were with things that we didn't learn. Any help is welcome.

- #2

ShayanJ

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- #3

HallsofIvy

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Perhaps your teacher was saying that

Either your teacher gave e^A= I+ A+ A^2/2+ A^3/3!+ ... (an infinite sum) from which it follows that if A^n= 0 for n> k that e^A= I+ A+ A^2/2+ A^3/3!+ ... + A^k/k! or your teacher, wishing to avoid the technical complications involved in defining infinite sums of matrices, just said that

In either case, it does not require "proof" because it is a

- #4

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Yes but how does that come out from the definition which he gave? :\

@HallsofIvy :

http://en.wikipedia.org/wiki/Exponential_matrix#Nilpotent_case

He basically gave that case, and asked us to prove what the inverse will be.

- #5

Office_Shredder

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This is not the matrix exponential. For example if A is diagonal then e

Gregory, if you've been assigned an exercise you should post the problem in the homework forum, with the full problem statement as you have been given it and the work you have done to try to solve it.

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