Refine
Document Type
- Article (2)
- Conference Proceeding (1)
Language
- English (3)
Has Fulltext
- yes (3) (remove)
Keywords
- Totally nonnegative matrix (3) (remove)
Institute
In 1970, B.A. Asner, Jr., proved that for a real quasi-stable polynomial, i.e., a polynomial whose zeros lie in the closed left half-plane of the complex plane, its finite Hurwitz matrix is totally nonnegative, i.e., all its minors are nonnegative, and that the converse statement is not true. In this work, we explain this phenomenon in detail, and provide necessary and sufficient conditions for a real polynomial to have a totally nonnegative finite Hurwitz matrix.
The class of square matrices of order n having a negative determinant and all their minors up to order n-1 nonnegative is considered. A characterization of these matrices is presented which provides an easy test based on the Cauchon algorithm for their recognition. Furthermore, the maximum allowable perturbation of the entry in position (2,2) such that the perturbed matrix remains in this class is given. Finally, it is shown that all matrices lying between two matrices of this class with respect to the checkerboard ordering are contained in this class, too.