Intuitively, a tensor is an object which has two attributes:

- invariant direction under a change of coordinates, and
- components which change in a ”special” way under a change of coordinates.

The idea is, that if you have some forward and backwards transformations be-

tween two coordinate basis, those transformations are inverses of one another

and behave consistently. In a more mathematically rigorous sense, a tensor

is defined as some set of vectors and covectors combined together under a

tensor product, hence the name ”tensor”.