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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Bibliographic Details
Published inLinear & multilinear algebra Vol. 55; no. 5; pp. 491 - 498
Main Authors Mashreghi, Javad, Rivard, Roland
Format Journal Article
LanguageEnglish
Published Taylor & Francis Group 01.09.2007
Subjects
2000 Mathematics Subject Classifications: Primary: 15A51
Doubly stochastic matrices
Eigenvalue
Secondary: 15A18
Spectrum
Stochastic matrices
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ISSN0308-1087
1563-5139
DOI10.1080/03081080600899296

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Summary: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 .
ISSN:0308-1087
1563-5139
DOI:10.1080/03081080600899296