  In this paper we discuss the mathematical background and the computational
aspects which underly the implementation of a collection of Julia functions in
the MatrixPencils package for the determination of structural properties of
polynomial and rational matrices. We primarily focus on the computation of the
finite and infinite spectral structures (e.g., eigenvalues, zeros, poles) as
well as the left and right singular structures (e.g., Kronecker indices), which
play a fundamental role in the structure of the solution of many problems
involving polynomial and rational matrices. The basic analysis tool is the
determination of the Kronecker structure of linear matrix pencils using
numerically reliable algorithms, which is used in conjunction with several
linearization techniques of polynomial and rational matrices. Examples of
polynomial and rational matrices, which exhibit all relevant structural
features, are considered to illustrate the main mathematical concepts and the
capabilities of implemented tools.
