|Title||Structural properties of polynomial and rational matrices, a survey.|
|Author(s)|| Juan C. Zu~niga-Anaya|
|Type||Article in Journal|
|Abstract||A review of the structural properties of polynomial and rational matrices is presented. After the analysis of the finite spectrum of a polynomial matrix A(λ), via the Smith canonical form, we analyze the infinity as an eigenvalue, but also as a pole or zero (via the Smith McMillan canonical form) when considering A(λ) in the set of rational matrices. Then we focus on the structures generated by the columns of A(λ). Here we review two different approaches: when considering linear combinations over|
the rational functions, and when linear combinations are supposed to be over polynomials only. The objective is to compare and contrast the results of these two lines of thought, as well as to underline the fundamental differences between matrix polynomials in one or several variables. Structure preserving transformations and equivalence relations over polynomial matrices are also reviewed.
|Keywords||matrix polynomials; eigenstructure; canonical forms; equivalence relations; modules; Gröbner basis;|
|Publisher||Hilaris Publishers, Ruse|