Rank-one corrections of nonnegative matrices, with an application to matrix population models (Q2923369)
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scientific article; zbMATH DE number 6356195
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Rank-one corrections of nonnegative matrices, with an application to matrix population models |
scientific article; zbMATH DE number 6356195 |
Statements
15 October 2014
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nonnegative matrix
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spectral radius
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second largest eigenvalue
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rank-one correction
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matrix population model
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projection matrix
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indicator function
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recruiting stage
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0.8804325
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0.8691611
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0.8544153
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0.8483716
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0.8458876
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0.8407068
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0.83280027
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0.8313329
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Rank-one corrections of nonnegative matrices, with an application to matrix population models (English)
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The authors study the location of the second largest eigenvalue of a nonnegative matrix and what occurs with such a number under rank-one corrections. The main result proves that if a matrix \(B\) is a rank-one correction of a matrix \(A\) (both nonnegative), then \(B\) has at most one real eigenvalue (which is simple) greater than the leading eigenvalue of \(A\). It is shown that the analogue of such result is not true for eigenvalue modulus or for the eigenvalue real parts. Such results are applicable to matrix population models where the location of the second largest positive eigenvalue plays a crucial role.
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