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In this paper we discuss the mathematical background and the computationalaspects which underly the implementation of a collection of Julia functions inthe MatrixPencils package for the determination of structural properties ofpolynomial and rational matrices. We primarily focus on the computation of thefinite and infinite spectral structures (e.g., eigenvalues, zeros, poles) aswell as the left and right singular structures (e.g., Kronecker indices), whichplay a fundamental role in the structure of the solution of many problemsinvolving polynomial and rational matrices. The basic analysis tool is thedetermination of the Kronecker structure of linear matrix pencils usingnumerically reliable algorithms, which is used in conjunction with severallinearization techniques of polynomial and rational matrices. Examples ofpolynomial and rational matrices, which exhibit all relevant structuralfeatures, are considered to illustrate the main mathematical concepts and thecapabilities of implemented tools.

On Computing the Kronecker Structure of Polynomial and Rational Matrices using Julia