Handbook of Linear Algebra, 2nd Edition

Chapter 34

Representations of Quivers and Mixed Graphs

Roger A. Horn

The University of Utah

Vladimir V. Sergeichuk

Institute of Mathematics, Ukraine

In Section 34.1, Section 34.2 and Section 34.3, we give an informal introduction to quivers from a linear algebraist's point of view. Exact definitions, results, and their proofs can be found in surveys [DW05, Sav06] and monographs [ASS06, ARS95, DR76, GR92, HGK07, Rin84]. After Gabriel's article [Gab72], in which the notions of a quiver and its representations were introduced, it became clear that a whole range of problems about systems of linear mappings can be formulated and studied in a uniform way. Quivers arise naturally in many areas of mathematics (representation theory, algebraic and differential ...