Level characteristics corresponding to peripheral eigenvalues of a nonnegative matrix |
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Authors: | Judith J McDonald DeAnne M Morris |
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Institution: | Box 643113, Department of Mathematics, Washington State University, Pullman, 99164-3113 WA, USA |
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Abstract: | In this paper, we give necessary and sufficient conditions for a set of Jordan blocks to correspond to the peripheral spectrum of a nonnegative matrix. For each eigenvalue, λ, the λ-level characteristic (with respect to the spectral radius) is defined. The necessary and sufficient conditions include a requirement that the λ-level characteristic is majorized by the λ-height characteristic. An algorithm which has been implemented in MATLAB is given to determine when a multiset of Jordan blocks corresponds to the peripheral spectrum of a nonnegative matrix. The algorithm is based on the necessary and sufficient conditions given in this paper. |
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Keywords: | Nonnegative matrix Eventually nonnegative matrix Peripheral spectrum Jordan form Level characteristic Height characteristic |
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