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rayman123
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Homework Statement
I am searching for a proof of convergence of matrix exponential series. Where I can find it?
Thanks!
Proof of Convergence of Matrix Exponential Series
- Thread starter rayman123
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- Exponential Matrix
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SUMMARY
The discussion centers on the proof of convergence for the matrix exponential series, specifically the series defined by \(\sum_{k=0}^{+\infty}{\frac{\|A^k\|}{k!}}\). User Micromass suggests using D'Alembert's Ratio test to check for convergence, while also proposing a comparison with the series expansion of \(e^{\|A\|}\). The conclusion reached is that the series converges absolutely, confirming the validity of the proposed methods.
PREREQUISITES- Understanding of matrix norms and properties
- Familiarity with series convergence tests, particularly D'Alembert's Ratio test
- Knowledge of matrix exponential functions
- Basic principles of mathematical analysis
- Study the application of D'Alembert's Ratio test in series convergence
- Explore the properties of matrix norms in detail
- Learn about the series expansion of exponential functions, particularly \(e^{\|A\|}\)
- Investigate other convergence tests applicable to matrix series
Mathematicians, students studying linear algebra, and researchers interested in the convergence properties of matrix functions.
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