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Topics in Matrix Analysis by Charles R. Johnson, Roger A. Horn

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Chapter 2

Stable matrices and inertia

2.0    Motivation

    The primary motivation for the study of stable matrices (matrices whose eigenvalues have negative real parts) stems from a desire to understand stability properties of equilibria of systems of differential equations. Questions about such equilibria arise in a variety of forms in virtually every discipline to which mathematics is applied—physical sciences, engineering, economics, biological sciences, etc. In each of these fields it is necessary to study the dynamics of systems whose state changes, according to some rule, over time and, in particular, to ask questions about the long-term behavior of the system. Thus, matrix stability, an initial tool in the study of such questions, is ...

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