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Some remarks on the resemblance theorems associated with various orthonormalization procedures
Author(s) -
Löwdin PerOlov
Publication year - 1993
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.560480403
Subject(s) - mathematical proof , mathematics , norm (philosophy) , operator (biology) , value (mathematics) , zero (linguistics) , symmetry (geometry) , pure mathematics , combinatorics , chemistry , statistics , linguistics , epistemology , philosophy , biochemistry , geometry , repressor , transcription factor , gene
A survey is given of the resemblance theorems associated with various types of orthonormalization procedures having different kinds of symmetry properties appearing in the current literature. It is shown that the proofs for the minimum properties are closely connected with the fact that the Hilbert–Schmidt norm of an operator is always nonnegative and has the lowest value equal to zero. © 1993 John Wiley & Sons, Inc.