## Chapter 3TENSORS

We know that intellectual food is sometimes more easily digested, if not taken in the most condensed form. It will be asked, To what extent can specialized notations be adopted with profit ? To this question we reply, *only experience can tell*.

F. CAJORI, *History of Mathematical Notations*, p. 77

### 3·01.

In this chapter we develop the theory of tensors in a simple and restricted form. In many branches of physics the tensor notation in this form provides a compact mathematical expression, and familiarity with it is a preparation for the complete theory, involving the use of oblique axes, curvilinear coordinates and space of more than three dimensions; it is also an introduction to the ideas of matrix algebra. General tensor theory ...