Ki Hang Kim. Boolean Matrix Theory and Applications 1982

Textbook in PDF format

Boolean matrices are square matrices over the Boolean algebra of order 2, represented by (0,1}, where 0 + 0 = 0, 0 + 1 = 1 + 0 = 1 + 1 = 1, 0.0 = 0.1 = 1 • 0 = 0 and 1.1 = 1. Such matrices, together with matrix operations defined in terms of the Boolean addition and multiplication, have important applications to several subjects in the mathematical sciences, including, for example, preference relations of individuals or groups in mathematical economics and switching theory in electrical engineering. In particular, Boolean matrices provide convenient notation and techniques for extremal set theory and several other subjects and applications.
In this book, Ki Hang Kim presents a survey of both the algebraic and the combinatorial aspects of Boolean matrix theory