Geodesic
Positive entries of stable matrices
The electronic journal of linear algebra, Tome 12 (2004-2005).

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

Summary: The question of how many elements of a real positive stable matrix must be positive is investigated. It is shown that any real stable matrix of order greater than 1 has at least two positive entries. Furthermore, for every stable spectrum of cardinality greater than 1 there exists a real matrix with that spectrum with exactly two positive elements, where all other elements of the matrix can be chosen to be negative.
Classification : 15A18, 15A29
Keywords: stable matrix, companion matrix, positive elementary symmetric functions 
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     author = {Friedland, Shmuel and Hershkowitz, Daniel and Rump, Siegfried M.},
     title = {Positive entries of stable matrices},
     journal = {The electronic journal of linear algebra},
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     volume = {12},
     year = {2004-2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2004-2005__12__a4/}
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Friedland, Shmuel; Hershkowitz, Daniel; Rump, Siegfried M. Positive entries of stable matrices. The electronic journal of linear algebra, Tome 12 (2004-2005). http://geodesic.mathdoc.fr/item/ELA_2004-2005__12__a4/