In this problem, we take | ·| to be the usual Euclidean 2-norm. Suppose that all the eigenvalues of the matrix A have negative real part. Then every solution of the differential equation x' Ax satisfies, |x(t)| < |x(s)|, if t > s.

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ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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Please give me a counter example because it is false

In this problem, we take |·| to be the usual Euclidean 2-norm.
Suppose that all the eigenvalues of the matrix A have negative real part. Then every
solution of the differential equation x'
Ax satisfies,
|æ(t)| < |x(s)|,
if t > s.
Transcribed Image Text:In this problem, we take |·| to be the usual Euclidean 2-norm. Suppose that all the eigenvalues of the matrix A have negative real part. Then every solution of the differential equation x' Ax satisfies, |æ(t)| < |x(s)|, if t > s.
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