Creation and annihilation in matrix theory

A closed form representation is given for the matrix S that sweeps out a single column. This includes the integer as well as the unitary and regular cases. The closed form is built up from the 2×2 case. The product rule for adjoints is used to show that the dual of this procedure is precisely the co...

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Bibliographic Details
Published in:Linear algebra and its applications 2000-01, Vol.305 (1), p.47-65
Main Authors: Hartwig, Robert E., Prasad, K.M.
Format: Article
Language:English
Subjects:
Adjoints
Brahma
Completion
Elimination
Shiva
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Summary:A closed form representation is given for the matrix S that sweeps out a single column. This includes the integer as well as the unitary and regular cases. The closed form is built up from the 2×2 case. The product rule for adjoints is used to show that the dual of this procedure is precisely the completion procedure, which completes a single column to a matrix B such that SB=BS= diagonal . This construction underlines the fact that the completion and elimination processes are complementary. By permuting rows suitably, the matrices may be assumed to be in lower Hessenberg form.
ISSN:0024-3795
1873-1856
DOI:10.1016/S0024-3795(99)00197-4