This table shows important examples of tensors on vector spaces and tensor fields on manifolds. The tensors are classified according to their type , where "n" is the number of contravariant indices, "m" is the number of covariant indices, and gives the total order of the tensor. For example, a bilinear form is the same thing as a -tensor; an inner product is an example of a -tensor, but not all -tensors are inner products. In the -entry of the table, "M" denotes the dimensionality of the underlying vector space or manifold because for each dimension of the space, a separate index is needed to select that dimension to get a maximally covariant antisymmetric tensor.