Definition:Dot Product/Einstein Summation Convention/Mistake

Source Work

 * Volume One:
 * Chapter $1$ Vectors in Classical Physics:
 * $1.3$ The Scalar Product
 * $1.3$ The Scalar Product

Mistake

 * We shall adopt Einstein's summation convention throughout this chapter. In terms of this convention we have, for example,


 * $\mathbf x \cdot \mathbf y = x_i y_j \delta_{i j} = x_i y_j = x_j y_j$

Correction
That third expression in the equality should read $x_i y_i$, not $x_i y_j$.