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Let an operator A have real, distinct eigenvalues. What condition on the eigen- alues is equivalent to lim | x(t) | = ∞ for every solution x (t) to x' = Ax?

Let an operator A have real, distinct eigenvalues. What condition on the eigen- alues is equivalent to lim | x(t) | = ∞ for every solution x (t) to x' = Ax?

Advanced Engineering Mathematics
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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Question about: LINE SYSTEMS: CONSTANT COEFFICIENTS, REAL EIGENVALUES

The answer has been given, please prove the process

4. Let an operator A have real, distinct eigenvalues. What condition on the eigen- values is equivalent to lim | x(t) | = ∞ for every solution x(t) to x' = Ax? 4. All eigenvalues are positive.
Transcribed Image Text:4. Let an operator A have real, distinct eigenvalues. What condition on the eigen- values is equivalent to lim | x(t) | = ∞ for every solution x(t) to x' = Ax? 4. All eigenvalues are positive.
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