1 - Notations and Cartesian Tensors

Abstract

It is convenient to use both “matrix” and “tensor notation” depending on the application. A matrix consists of a collection of certain quantities that are termed the “components” of the matrix. The components are ordered in rows and columns. If the number of rows or columns is equal to one, the matrix is one-dimensional; otherwise it is two-dimensional. As index notation is an integrated part of tensor algebra, this chapter illustrates the advantage of this notation. Index notation is often used in tensor algebra, and it is therefore often termed as “tensor notation.” Index notation implies that complicated expressions can be written in a very compact fashion that emphasizes the physical content of these expressions and greatly facilitates mathematical manipulations. The chapter provides an elementary discussion of the concept of tensors and why they appear in a natural manner when formulating physical relations.