ABSTRACT
In this chapter, we present some results on matrices over integral domains, which extend the well-known results for matrices over the fields discussed in Chapter 1 of this book. The general theory of linear algebra over commutative rings is extensively studied in the book [McD84]. It is mostly intended for readers with a thorough training in ring theory. The aim of this chapter is to give a brief survey of notions and facts about matrices over classical domains that come up in applications. Namely over the ring of integers, the ring of polynomials over the field, the ring of analytic functions in one variable on an open connected set, and germs of analytic functions in one variable at the origin. The last section of this chapter is devoted to the notion of strict equivalence of pencils.
