2020/03/05 by Javier J. Pérez, Pérez, Javier, María C. Quintana +1
Computer Science · Mathematics · #15A18 #15A22 #15A54 #65F15 #93B18 #93B60 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2003.02934
openalex publication_date 2020/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a new family of linearizations of rational matrices R(λ) written in the general form R(λ)= D(λ)+C(λ)A(λ)-1B(λ), where D(λ), C(λ), B(λ) and A(λ) are polynomial matrices. Such representation always exists and are not unique. The new linearizations are constructed from linearizations of the polynomial matrices D(λ) and A(λ), where each of them can be represented in terms of any polynomial basis. In addition, we show how to recover eigenvectors, when R(λ) is regular, and minimal bases and minimal indices, when R(λ) is singular, from those of their linearizations in this family.