Hi all, I am trying to self-learn continuum mechanics, and I have a question regarding the development of the deformation gradient (which ultimately leads to green's deformation tensor). I have attached the specifics of the question in a attached photo. Ultimately, there comes a point when determining the deformation using the change in magnitude of the square of dX and dx: dx^2 - dX^2 = dxidxi-dXadXa However, somehow using a previous equation (dxi = xi,adXa) and the susbtitution property of the kronecker delta, they come up with: dx^2 - dX^2 = xi,adXa*xi,bdXb - delta(ab)*dXa*dXb My question is - how was the kronecker delta substituted in? There is no direction associated with magnitudes. Further - where did the subscript "B" come from and what does it represent physically? Any help would be greatly appreciated.