Definition:Dot Product/Einstein Summation Convention/Mistake
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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
- Chapter $1$ Vectors in Classical Physics:
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
- 1992: Frederick W. Byron, Jr. and Robert W. Fuller: Mathematics of Classical and Quantum Physics ... (previous) ... (next): Volume One: Chapter $1$ Vectors in Classical Physics: $1.3$ The Scalar Product