Editing Cartan matrix (section)

== Representations of finite-dimensional algebras ==
In [[modular representation theory]], and more generally in the theory of representations of finite-dimensional [[associative algebra]]s ''A'' that are ''not'' [[Semisimple algebra|semisimple]], a '''Cartan matrix''' is defined by considering a (finite) set of [[principal indecomposable module]]s and writing [[composition series]] for them in terms of [[irreducible module]]s, yielding a matrix of integers counting the number of occurrences of an irreducible module.