A Gerschgorin theorem for linear difference equations and eigenvalues of matrix products |
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Authors: | Dennis D. Berkey |
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Affiliation: | Department of Mathematics Miami University Oxford, Ohio 45056, USA |
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Abstract: | The Gerschgorin circle theorem is used here to give sufficient conditions for the solution space of the difference equation x(m+1) = A (m+1)x(m) to admit a type of exponential dichotomy. The result obtained is then used to establish a result on regions of eigenvalue inclusion for the product of finitely many square matrices. An application to differential equations is also given. |
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