Transitioning from Stage 2 to Stage 3

LCSphysicist · Nov 19, 2020

$Equation chain: sum over i of (dx^i)^2 equals sum over i, k, j of R^{ik} dx^k R^{ij} dx^j, which equals sum over j of (dx^j)^2, which equals sum over k, j of delta^{kj} dx^k dx^j.$

My problem is how to go from the second to the third.

PeroK · Nov 19, 2020

Herculi said:

Homework Statement:: I was studying transformations/rotations in a plane, but i am having trouble to understand the image on the black table. dx' is dx in a rotated frame and R is the rotation matrix
Relevant Equations:: \n

View attachment 272773
My problem is how to go from the second to the third.

A rotation matrix is orthogonal.

Transitioning from Stage 2 to Stage 3

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