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Is there any relationship between the derivative of a matrix which depend by a parameter and its eigenvalues?

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    $\begingroup$ Take the matrix $A(t)=(a)$ with $a\in\mathbb{R}$, than its derivative in respect to $t$ is obviously zero, and the eigenvalue of the matrix is $a$, so there is no relationship $\endgroup$ – Dominic Michaelis Mar 5 '13 at 13:39
  • $\begingroup$ I'm searching for a result which connect the definite positiveness of the matrix derivative with its eigenvalues. $\endgroup$ – Mario Mar 5 '13 at 13:44
  • $\begingroup$ The eigenvalues of the derivative, or the eigenvalues of the original matrix? $\endgroup$ – Martin Argerami Mar 8 '13 at 15:15
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The eigenvalues will be a function of the parameter too and you can write down the differential equations that govern their motion as a function of that parameter. You might want to look at: Section III: Dynamics of eigenvalues in http://arxiv.org/abs/1404.4113 Best, Ramis

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