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.
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.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.1: Eigenvalues And Eigenvectors
Problem 80E
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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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