Equivalent definitions of tensors on finite dimensional spaces.

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:

1. A tensor is a bilinear mapping from $V \times W$ into the field $K$
2. A tensor is a bilinear mapping from $V^*\times W^*$ into the field $K$
3. A tensor is an element of the tensor product $V \otimes W$

Why are they equivalent?

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–  Hans Lundmark Jan 14 '13 at 19:25