Quantum Formalism and Information Retrieval

In 2004 Keith van Rijsbergen published a book with the title "The Geometry of Information Retrieval". In this book he suggested that quantum formalism can be successfully used to model some of the problems of Information Retrieval. This book was given to me by my colleague Dr. Vasudev Varma of the International Institute of Information Technology, Hyderabad with a request to offer a course on the ideas of the book.

Last semester I did so. I had hoped for senior students who already knew Linear Algebra, but none of those who joined was clear about the basics of Linear Algebra. So almost the entire course was spent teaching them linear algebra and then some of the basics of quantum terminology. At the end I was left with only one class to explain how quantum formalism relates to Information Retrieval.

There was another difficulty. The book of Rijsbergen used the physics notation for the inner product according to which it is the second term of the inner product that is linear and the first term antilinear. The mathematics text books have the opposite convention. So there was a need to rewrite the basics of Hilbert Space theory in the mathematical tradition but using the physics notation. This is now summarized in a document and attached here as Review of Hilbert Space Theory. Also attached is my write-up on the Hilbert Space Model for Information Retrieval.