A tensor may be represented as a (potentially multidimensional) array. Just as a vector in an n - dimensional space is represented by a one-dimensional array with n components with respect to a given basis, any tensor with respect to a basis is represented by a multidimensional array. For example, a linear operator is represented in a basis as a two-dimensional square n × n array. The numbers in the multidimensional array are known as the components of the tensor. They are denoted by indices giving their position in the array, as subscripts and superscripts, following the symbolic name of the tensor. For example, the components of an order 2 tensor T could be denoted T ij , where i and j are indices running from 1 to n, or also by T j. Whether an index is displayed as a superscript or subscript depends on the transformation properties of the tensor, described below. Thus while T ij and T j can both be expressed as n -by- n matrices, and are numerically related via index juggling, the difference in their transformation laws indicates it would be improper to add them together.