The tensor algebra T ⁡ ⁡ ( V ) is a formal way of adding products to any vector space V to obtain an algebra. As a vector space, it is spanned by symbols, called simple tensors v 1 ⊗ ⊗ v 2 ⊗ ⊗ ⋯ ⋯ ⊗ ⊗ v n , where the degree n varies. The multiplication is given by concatenating such symbols, imposing the distributive law under addition, and requiring that scalar multiplication commute with the tensor product ⊗, much the same way as with the tensor product of two vector spaces introduced in the above section on tensor products. In general, there are no relations between v 1 ⊗ ⊗ v 2 and v 2 ⊗ ⊗ v 1 . Forcing two such elements to be equal leads to the symmetric algebra, whereas forcing v 1 ⊗ ⊗ v 2 = − − v 2 ⊗ ⊗ v 1 yields the exterior algebra.