If a coordinates are given, then they will be given with respect to a basis. However, it's entirely possible to do things more abstractly without introducing co

If a coordinates are given, then they will be given with respect to a basis. However, it's entirely possible to do things more abstractly without introducing coordinates and bases to begin with, for example: https://en.wikipedia.org/wiki/Tensor_(intrinsic_definition) https://en.wikipedia.org/wiki/Tensor_(intrinsic_definition)