On symmetric matrices with exactly one positive eigenvalue
ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 158-167.

Voir la notice de l'article dans Electronic Library of Mathematics

Summary: We present a class of nonsingular matrices, the M C $^{\prime}$ -matrices, and prove that the class of symmetric M C-matrices introduced by Shen, Huang and Jing [On inclusion and exclusion intervals for the real eigenvalues of real matrices. SIAM J. Matrix Anal. Appl., 31:816-830, 2009] and the class of symmetric M C $^{\prime}$ -matrices are both subsets of the class of symmetric matrices with exactly one positive eigenvalue. Some other sufficient conditions for a symmetric matrix to have exactly one positive eigenvalue are derived.
Classification : 15A18, 15A48, 15A57
Mots-clés : eigenvalue, symmetric matrix, M C-matrix, M C $^{\prime}$ -matrix 
@article{EEJLA_2010__20__a42,
     author = {Shen, Shu-Qian and Huang, Ting-Zhu},
     title = {On symmetric matrices with exactly one positive eigenvalue},
     journal = {ELA. The Electronic Journal of Linear Algebra},
     pages = {158--167},
     publisher = {mathdoc},
     volume = {20},
     year = {2010},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a42/}
}
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Shen, Shu-Qian; Huang, Ting-Zhu. On symmetric matrices with exactly one positive eigenvalue. ELA. The Electronic Journal of Linear Algebra, Tome 20 (2010), pp. 158-167. https://geodesic-test.mathdoc.fr/item/EEJLA_2010__20__a42/