Proof of Convergence of Matrix Exponential Series

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    Exponential Matrix
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Homework Help Overview

The discussion revolves around the convergence of the matrix exponential series, specifically seeking a proof for its absolute convergence.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the absolute convergence of the series and suggest using D'Alembert's Ratio test as a potential method for analysis. Others propose comparing the series to the expansion of e^{\|A\|} as an alternative approach.

Discussion Status

The conversation is active, with participants exploring different methods to establish convergence. Some guidance has been offered regarding potential tests and comparisons, but no consensus has been reached on a specific approach.

Contextual Notes

There is an emphasis on proving convergence, and the original poster is looking for resources or proofs related to this topic.

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Homework Statement


I am searching for a proof of convergence of matrix exponential series. Where I can find it?
Thanks!



Homework Equations





The Attempt at a Solution

 
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Can you show that the series converges absolutely? I.e. that

[tex]\sum_{k=0}^{+\infty}{\frac{\|A^k\|}{k!}}[/tex]

converges...
 
@Micromass : As a sidenote, can this expression be checked for convergence/divergence using D'Alembert's Ratio test?
 
Probably yes, but I prefer to compare it with the series expansion of [tex]e^{\|A\|}[/tex]...
 
I found the whole proof
 

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