This book begins and ends in information retrieval, but travels through a route constructed in an abstract way. In particular it goes through some of the most interesting and important models for information retrieval, a vector space model, a probabilistic model and a logical model, and shows how these three and possibly others can be described and represented in Hilbert space. The reasoning that occurs within each one of these models is formulated algebraically and can be shown to depend essentially on the geometry of the information space. The geometry can be seen as a ‘language’ for expressing the different models of information retrieval.

The approach taken is to structure these developments firmly in terms of the mathematics of Hilbert spaces and linear operators. This is of course the approach used in quantum mechanics. It is remarkable that the application of Hilbert space mathematics to information retrieval is very similar to its application to quantum mechanics. A document in IR can be represented as a vector in Hilbert space, and an observable such as ‘relevance’ or ‘aboutness’ can be represented by a Hermitian operator. However, this is emphatically not a book about quantum mechanics but about using the same language, the mathematical language of quantum mechanics, for the description of information retrieval. It turns out to be very convenient that quantum mechanics provides a ready-made interpretation of this language.