Boolean matrix

(In some contexts, particularly computer science, the term "Boolean matrix" implies this restriction.)

Let U be a non-trivial Boolean algebra (i.e. with at least two elements).

Intersection, union, complementation, and containment of elements is expressed in U.

The intersection or union of two such matrices is obtained by applying the operation to entries of each pair of elements to obtain the corresponding matrix intersection or union.

The product of two Boolean matrices is expressed as follows:

{\displaystyle (AB)_{ij}=\bigcup _{k=1}^{n}(A_{ik}\cap B_{kj}).}

According to one author, "Matrices over an arbitrary Boolean algebra β satisfy most of the properties over β0 = {0, 1}.