A rank-reduced, singular value decomposition is performed on the matrix to determine patterns in the relationships between the terms and concepts contained in the text. The SVD forms the foundation for LSI. It computes the term and document vector spaces by approximating the single term-frequency matrix, formula_68, into three other matrices— an m by r term-concept vector matrix formula_82, an r by r singular values matrix formula_83, and a n by r concept-document vector matrix, formula_84, which satisfy the following relations: