Geodesic
On one class of positive matrices with minors of different signs
Trudy Instituta matematiki, Tome 17 (2009) no. 1, pp. 79-89

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A new class of sign-symmetric matrices is introduced in this paper. Such matrices are named strictly $\mathcal J$-sign-symmetric. The existence of the second (according to the module) positive simple eigenvalue $\lambda_2$ of a positive matrix $A$ is proved under the additional condition, that its compound matrix belongs to the introduced class of strictly $\mathcal J$-sign-symmetric matrices. 
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     author = {O. Y. Kushel},
     title = {On one class of positive matrices with minors of different signs},
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O. Y. Kushel. On one class of positive matrices with minors of different signs. Trudy Instituta matematiki, Tome 17 (2009) no. 1, pp. 79-89. http://geodesic.mathdoc.fr/item/TIMB_2009_17_1_a7/