Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Prologue -- Scene -- 1 Introduction -- Further reading -- 2 On sets and kinds for IR -- Elementary IR -- Inverted files and natural kinds -- Definition D1 -- Definition D2 -- Definition D3 -- Definition D4 -- Definition D5 -- Definition D6 -- Further reading -- 3 Vector and Hilbert spaces -- Step 1 -- Step 2 -- Further reading -- 4 Linear transformations, operators and matrices -- Projectors -- Eigenvalues and eigenvectors -- Spectral theorem -- Further reading -- 5 Conditional logic in IR -- Compatibility -- Stalnaker conditional -- Further reading -- 6 The geometry of IR -- Preliminaries: D-notation -- The trace -- Density operators -- Gleason's Theorem -- Definition -- Theorem -- Interpreting tr(.) -- Co-ordination level matching -- Pseudo-relevance feedback -- Relevance feedback -- Dynamic clustering -- Ostensive retrieval -- Further reading and future research -- Appendix I Linear algebra -- Vector space -- Hilbert space -- Operators -- Linear functionals -- Dirac notation -- Dyads -- Useful identities in Dirac notation -- Cauchy-Schwartz inequality -- Appendix II Quantum mechanics -- Physical states -- Observables -- Measurements -- Heisenberg Uncertainty Principle -- Further reading -- Appendix III Probability -- Classical probability -- Quantum probability -- Further reading -- Bibliography -- Author index -- Index.