On a conjecture about the eigenvalues of doubly stochastic matrices
According to a long standing conjecture, the geometric location of eigenvalues of doubly stochastic matrices of order n is exactly the union of regular k-gons anchored at 1 in the unit disc for 2 ≤ k ≤ n. It is easy to verify this fact for n = 2 , 3 . But, for n ≥ 4, it has been an open question....
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| Published in | Linear & multilinear algebra Vol. 55; no. 5; pp. 491 - 498 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Taylor & Francis Group
01.09.2007
|
| Subjects | |
| Online Access | Get full text |
| ISSN | 0308-1087 1563-5139 |
| DOI | 10.1080/03081080600899296 |
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| Abstract | According to a long standing conjecture, the geometric location of eigenvalues of doubly stochastic matrices of order n is exactly the union of regular k-gons anchored at 1 in the unit disc for 2 ≤ k ≤ n. It is easy to verify this fact for n =
2
,
3
. But, for n ≥ 4, it has been an open question. We show that this conjecture is wrong for n =
5
. |
|---|---|
| AbstractList | According to a long standing conjecture, the geometric location of eigenvalues of doubly stochastic matrices of order n is exactly the union of regular k-gons anchored at 1 in the unit disc for 2 ≤ k ≤ n. It is easy to verify this fact for n =
2
,
3
. But, for n ≥ 4, it has been an open question. We show that this conjecture is wrong for n =
5
. |
| Author | Rivard, Roland Mashreghi, Javad |
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| CitedBy_id | crossref_primary_10_1016_j_laa_2017_01_009 crossref_primary_10_1016_j_laa_2009_09_002 crossref_primary_10_1016_j_laa_2021_12_011 crossref_primary_10_1016_j_laa_2024_10_020 crossref_primary_10_1090_S0002_9939_2014_12412_9 crossref_primary_10_1080_03081087_2022_2064966 crossref_primary_10_1007_s41980_024_00925_5 crossref_primary_10_1016_j_laa_2020_01_018 crossref_primary_10_1080_10586458_2020_1727799 crossref_primary_10_3390_sym12030369 crossref_primary_10_2478_jamsi_2021_0005 crossref_primary_10_1016_j_laa_2018_01_016 |
| Cites_doi | 10.1007/BF01313442 10.1016/S0024-3795(97)00018-9 10.1007/978-3-642-67131-9 10.1007/BF02546519 |
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| Copyright | Copyright Taylor & Francis Group, LLC 2007 |
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| SubjectTerms | 2000 Mathematics Subject Classifications: Primary: 15A51 Doubly stochastic matrices Eigenvalue Secondary: 15A18 Spectrum Stochastic matrices |
| Title | On a conjecture about the eigenvalues of doubly stochastic matrices |
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