Geodesic
A note on the convexity of the realizable set of eigenvalues for nonnegative symmetric matrices
The electronic journal of linear algebra, Tome 8 (2001), pp. 110-114.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Geometric properties of the set Rn of n-tuples of realizable spectra of nonnegative symmetric matrices, and the Soules set Sn introduced by McDonald and Neumann, are examined. It is established that S5 is properly contained in R5. Two interesting examples are presented which show that neither Rn nor Sn need be convex. It is proved that Rn and Sn are star convex and centered at (1, 1, . . . , 1).
Classification : 15A18, 15A29, 15A57
Keywords: symmetric matrices, inverse eigenvalue problem, realizable set, soules set 
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     author = {Knudsen, C. and McDonald, J.J.},
     title = {A note on the convexity of the realizable set of eigenvalues for nonnegative symmetric matrices},
     journal = {The electronic journal of linear algebra},
     pages = {110--114},
     publisher = {mathdoc},
     volume = {8},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2001__8__a3/}
}
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Knudsen, C.; McDonald, J.J. A note on the convexity of the realizable set of eigenvalues for nonnegative symmetric matrices. The electronic journal of linear algebra, Tome 8 (2001), pp. 110-114. http://geodesic.mathdoc.fr/item/ELA_2001__8__a3/