I have recently been studying various texts on differential geometry, and I am quite puzzled that various authors define the notion of a tensor quite differently. I have come across the following defintions:
- A tensor is a bilinear mapping from $V \times W$ into the field $K$
- A tensor is a bilinear mapping from $V^*\times W^*$ into the field $K$
- A tensor is an element of the tensor product $V \otimes W$
Why are they equivalent?
