An Algorithm for Factoring Hermitian Matrix Polynomials Relative to the Imaginary Axis

1996 ◽  
Vol 29 (1) ◽  
pp. 1263-1268
Author(s):  
Chyi Hwang ◽  
Bo-Win Lin ◽  
Tong-Yi Guo
Keyword(s):  
Imaginary Axis ◽  
Hermitian Matrix ◽  
Matrix Polynomials

scholarly journals A Schur-Cohn theorem for matrix polynomials

1990 ◽  
Vol 33 (3) ◽  
pp. 337-366 ◽  
Author(s):  
Harry Dym ◽  
Nicholas Young
Keyword(s):  
Unit Circle ◽  
Matrix Polynomial ◽  
Hermitian Matrix ◽  
Krein Space ◽  
Gram Matrix ◽  
Natural Basis ◽  
Test Matrix ◽  
Matrix Polynomials ◽  
Rational Vector ◽  
Square Matrix

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.

scholarly journals Linearizations of Hermitian Matrix Polynomials Preserving the Sign Characteristic

2017 ◽  
Vol 38 (1) ◽  
pp. 249-272 ◽  
Author(s):  
María I. Bueno ◽  
Froilán M. Dopico ◽  
Susana Furtado
Keyword(s):  
Hermitian Matrix ◽  
Matrix Polynomials

scholarly journals On the sign characteristics of Hermitian matrix polynomials

2016 ◽  
Vol 511 ◽  
pp. 328-364 ◽  
Author(s):  
Volker Mehrmann ◽  
Vanni Noferini ◽  
Françoise Tisseur ◽  
Hongguo Xu
Keyword(s):  
Hermitian Matrix ◽  
Matrix Polynomials

On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

2020 ◽  
pp. 445-454
Author(s):  
Deepali Khurana ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Imaginary Axis ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

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