(from A. Greenbaum) For A € Rmxm, define the matrix exponential: A² A³ 2! 3! Ak k! e^=1+A+ + e²A = Suppose A is diagonalizable: A = XAX ¹. Show that e¹A = e²x₁ em ΣΑ k= XeX 1, where
(from A. Greenbaum) For A € Rmxm, define the matrix exponential: A² A³ 2! 3! Ak k! e^=1+A+ + e²A = Suppose A is diagonalizable: A = XAX ¹. Show that e¹A = e²x₁ em ΣΑ k= XeX 1, where
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. (from A. Greenbaum) For A € Rmxm, define the matrix exponential:
A² A³
e^ = I + A+ + +... =
2! 3!
Σ
k=0
Suppose A is diagonalizable: A = XAX ¹. Show that elA = XeAX-1, where
e²d₂
+²
=
e²A
k!
elam
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