In the example in Fig. 6 .3, the document vectors are of dimension 4, dimension just so they fit on the page; in real term-document matrices, the vectors representing each document would have dimensionality |V |, the vocabulary size. The ordering of the numbers in a vector space indicates different meaningful dimensions on which documents vary. Thus the first dimension for both these vectors corresponds to the number of times the word battle occurs, and we can compare each dimension, noting for example that the vectors for As You Like It and Twelfth Night have similar values (1 and 0, respectively) for the first dimension. Figure 6 .3 The term-document matrix for four words in four Shakespeare plays. The red boxes show that each document is represented as a column vector of length four.