Elementary divisors of induced transformations on tensors via the representation theory of sl 2 |
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Authors: | Michael A Gauger |
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Institution: | Department of Mathematics and Statistics , University of Massachusetts , Amherst, Mass, 01002 |
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Abstract: | We study various stability type conditions on a matrix A related to the consistency of the Lyapunov equation AD+DAt positive definite, where D is a positive diagonal matrix. Such problems arise in mathematical economics, in the study of time-invariant continuous-time systems and in the study of predator-prey systems. Using a theorem of the alternative, a characterization is given for all A satisfying the above equation. In addition, some necessary conditions for consistency and some related ideas are discussed. Finally, a method for constructing a solution D to the equation is given for matrices A satisfying certain conditions. |
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Keywords: | AMS (MOS) Subject classification: 15A15 15A48 34D25 65F15 |
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