Extremal numbers of positive entries of imprimitive nonnegative matrices |
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| Authors: | Xingzhi Zhan |
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| Institution: | Department of Mathematics, East China Normal University, Shanghai 200062, China |
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| Abstract: | We determine the maximum and minimum numbers of positive entries of imprimitive nonnegative matrices with a given imprimitivity index. One application of the results is to estimate the imprimitivity index by the number of positive entries. The proofs involve the study of a cyclic quadratic form. This completes a research initiated by Lewin in 1990. |
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| Keywords: | 15A48 05D99 |
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