Definition:Dot Product/Einstein Summation Convention/Mistake

From ProofWiki
Jump to navigation Jump to search

Source Work

1992: Frederick W. Byron, Jr. and Robert W. Fuller: Mathematics of Classical and Quantum Physics:

Volume One:
Chapter $1$ Vectors in Classical Physics:
$1.3$ 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 $x_i y_j$.


Sources