Abstract
This chapter discusses elementary operations on vectors. The elementary operations are as fundamental in linear algebra as the operations of differentiation and integration are in the calculus. These elementary operations are indispensable both in the development of the theory of linear algebra and in the applications of this theory. In many treatments of linear algebra, the elementary operations are introduced after the development of a certain amount of matrix theory, and the matrix theory is used as a tool in establishing the properties of the elementary operations. The elementary operations are introduced as operations on sets of vectors and many of the results in matrix theory are developed with the aid of one's knowledge of elementary operations. The application of a sequence of elementary operations can be used to replace a given set A by a set A’ which has a simpler appearance. The chapter discusses the properties that A and A’ have in common. When these properties are known, one shall see that the elementary operations can be chosen so as to make the set A’ display certain important information concerning A.
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