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A Schur-Cohn theorem for matrix polynomials
| Content Provider | Scilit |
|---|---|
| Author | Dym, Harry Young, Nicholas |
| Copyright Year | 1990 |
| Description | Let N(λ) be a square matrix polynomial, and suppose det N is a polynomial of degree d. Subject to a certain non-singularity condition we construct a d by d Hermitian matrix whose signature determines the numbers of zeros of N inside and outside the unit circle. The result generalises a well known theorem of Schur and Cohn for scalar polynomials. The Hermitian “test matrix” is obtained as the inverse of the Gram matrix of a natural basis in a certain Krein space of rational vector functions associated with N. More complete results in a somewhat different formulation have been obtained by Lerer and Tismenetsky by other methods. |
| Related Links | https://www.cambridge.org/core/services/aop-cambridge-core/content/view/5AB9F1B5788EC10C3C510CB2218B26FE/S0013091500004806a.pdf/div-class-title-a-schur-cohn-theorem-for-matrix-polynomials-div.pdf |
| Ending Page | 366 |
| Page Count | 30 |
| Starting Page | 337 |
| ISSN | 00130915 |
| e-ISSN | 14643839 |
| DOI | 10.1017/s0013091500004806 |
| Journal | Proceedings of the Edinburgh Mathematical Society |
| Issue Number | 3 |
| Volume Number | 33 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 1990-10-01 |
| Access Restriction | Open |
| Subject Keyword | Proceedings of the Edinburgh Mathematical Society Applied Mathematics Schur Cohn Matrix Polynomial |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
