Abstract

Rectangular arrays are a useful notational convenience in recording the results of elementary operations on a set of vectors. These rectangular arrays are specific examples of the more general concept of a matrix over a set ℳ. This chapter presents a definition of the operation of multiplication on matrices with real numbers as elements and establishes the basic properties of this operation. The term matrix of transition applies only to situations involving nonempty finite sets of vectors, and these sets must be ordered. Whenever a set of vectors is listed without indices, it is understood that the index j is to go with the jth vector from the left. Thus, the first vector from the left is to have index 1, the second from the left to have index 2, and so on. The chapter describes the various properties of matrix multiplication and invertible matrices.

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