Prerequisites From Analysis

The word denumerable in the sequel means finite or countably infinite. Let M and N be two non-empty denumerable sets. A matrix is a function with domain the set of ordered pairs (m, n), where m ∈ M and n ∈ N,and with range a subset of the extended real number system—the reals with +∞ and −∞ adjoined. We call the sets M and N index sets. The matrix is called a finite matrix if both M and N are finite sets.