Talk:Tensors/Transformation rule under a change of basis
Perhaps this could be added... it seems some are confusing the change in the expression of the components of a tensor with the tensor itself, and thus they claim a tensor quantity changes under change of basis.
https://www.quora.com/A-change-of-basis-doesnt-change-the-properties-of-a-tensor-transformation-its-still-the-same-function-just-written-differently-Is-that-whats-meant-by-the-definition-of-tensors-as-objects-that-retain-their-meaning "If we then use a second basis of V, as you say, the tensor is the same, but its expression relative to the second basis is not the same as the one relative to the first one (in general)." "The coordinates of the tensor change under the change of basis transforms T and S in (1). However, the tensor itself is invariant (as would be a vector)."