Open AccessSimple necessary conditions for Hadamard factorizability of Hurwitz polynomials
Author(s) -
Stanisław Białas,
Michał Góra
Publication year - 2021
Publication title -
the electronic journal of linear algebra
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.447
H-Index - 31
eISSN - 1537-9582
pISSN - 1081-3810
DOI - 10.13001/ela.2021.5957
Subject(s) - mathematics , hadamard transform , factorization , hurwitz polynomial , simple (philosophy) , hadamard's maximal determinant problem , hadamard three lines theorem , complex hadamard matrix , hurwitz matrix , hadamard's inequality , hadamard product , focus (optics) , difference polynomials , hadamard matrix , pure mathematics , combinatorics , orthogonal polynomials , polynomial , mathematical analysis , algorithm , parametric statistics , philosophy , statistics , physics , epistemology , optics
In this paper, we focus the attention on the Hadamard factorization problem for Hurwitz polynomials. We give a new necessary condition for Hadamard factorizability of Hurwitz stable polynomials of degree $n\geq 4$ and show that for $n= 4$ this condition is also sufficient. The effectiveness of the result is illustrated during construction of examples of stable polynomials that are not Hadamard factorizable.