Premium
The projection operator for a space spanned by a linearly dependent set
Author(s) -
Berrondo Manuel,
Löwdin PerOlov
Publication year - 1969
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.560030604
Subject(s) - projection (relational algebra) , operator (biology) , set (abstract data type) , mathematics , metric (unit) , space (punctuation) , matrix (chemical analysis) , combinatorics , pure mathematics , mathematical analysis , algorithm , chemistry , computer science , biochemistry , operations management , repressor , chromatography , transcription factor , economics , gene , programming language , operating system
The explicit form of a projection operator constructed from a linearly dependent set is found. The relationships with canonical orthonormalization and with the cofactor matrix of the set's metric matrix are discussed. Similar expressions are obtained for the inner projection of a positive definite operator using a linearly dependent set.