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Completeness and linear independence of basis sets used in quantum chemistry
Author(s) -
Klahn Bruno,
Bingel Werner A.
Publication year - 1977
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560110607
Subject(s) - completeness (order theory) , independence (probability theory) , hilbert space , orthonormality , mathematics , dimension (graph theory) , basis (linear algebra) , measure (data warehouse) , orthonormal basis , pure mathematics , quantum mechanics , mathematical analysis , physics , statistics , computer science , geometry , database
Abstract Infinite sets of functions in Hilbert space are characterized by their completeness properties and the extent of linear independence. Different measures of linear independence such as orthonormality, Gram's determinant, the special measure of linear independence, and the asymptotic dimension are related to each other and with the degrees of completeness such as overcompleteness, exact completeness, and incompleteness as far as possible.