Row stochastic inverse eigenvalue problem
<p>Abstract</p> <p>In this paper, we give sufficient conditions or realizability criteria for the existence of a row stochastic matrix with a given spectrum Λ = {<it>λ</it><sub>1</sub>, ..., <it>λ<sub>n</sub></...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-01-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2011/1/24 |
| Summary: | <p>Abstract</p> <p>In this paper, we give sufficient conditions or realizability criteria for the existence of a row stochastic matrix with a given spectrum Λ = {<it>λ</it><sub>1</sub>, ..., <it>λ<sub>n</sub></it>} = Λ<sub>1 </sub>∪ ⋯ ∪ Λ<it><sub>m </sub></it>∪ Λ<sub><it>m</it>+1</sub>, <it>m > </it>0; where <inline-formula><graphic file="1029-242X-2011-24-i1.gif"/></inline-formula> (<it>p<sub>k </sub></it>is an integer greater than 1), <it>λ</it><sub><it>k</it>1 </sub>= <it>λ<sub>k </sub>> </it>0, 1 = <it>λ</it><sub>1 </sub>≥ <it>ω<sub>k </sub>> </it>0, <it>k </it>= 1, ..., <it>m</it>; Λ<sub><it>m</it>+1 </sub>= {<it>λ<sub>m</sub></it>+1}, <it>ω</it><sub><it>m</it>+1 </sub>≡ <it>λ</it><sub>1 </sub>+ ..., +<it>λ<sub>n </sub></it>≤ <it>λ</it><sub>1</sub>, <it>ω<sub>k </sub></it>≥ <it>λ<sub>k</sub></it>, <it>ω</it><sub>1 </sub>≥ <it>λ<sub>k</sub></it>, <it>k </it>= 2, ..., <it>m </it>+ 1. In the case when <it>p</it><sub>1</sub>, ..., <it>p<sub>m </sub></it>are all equal to 2, Λ becomes a list of 2<it>m </it>+ 1 real numbers for any positive integer <it>m</it>, and our result gives sufficient conditions for a list of 2<it>m </it>+ 1 real numbers to be realizable by a row stochastic matrix.</p> <p><b>AMS classification: </b>15A18.</p> |
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| ISSN: | 1025-5834 1029-242X |