The contraction can also be understood using the definition of a tensor as an element of a tensor product of copies of the space V with the space V by first decomposing the tensor into a linear combination of simple tensors, and then applying a factor from V to a factor from V. For example, a tensor T ∈ ∈ V ⊗ ⊗ V ⊗ ⊗ V ∗ ∗ can be written as a linear combination