- #1
Coffee_
- 259
- 2
Why is it so that I can write:
##x'_i=A_{ij}x_j## where ##A_{ij}=\frac{\partial x'_i}{\partial x_j}##?
Yes if the first expression is assumed it is clear to me why the coefficients have to be the partial derivatives, but why can we assume that we can always write it in a linear fashion in the first place? I assume this is something similar to any function being linearly apporximated close enough to a point but I'd like to hear it to be sure.
##x'_i=A_{ij}x_j## where ##A_{ij}=\frac{\partial x'_i}{\partial x_j}##?
Yes if the first expression is assumed it is clear to me why the coefficients have to be the partial derivatives, but why can we assume that we can always write it in a linear fashion in the first place? I assume this is something similar to any function being linearly apporximated close enough to a point but I'd like to hear it to be sure.