Creation and annihilation in matrix theory

Robert E. Hartwig, K. M. Prasad

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish
Pages (from-to)47-65
Number of pages19
JournalLinear Algebra and Its Applications
Volume305
Issue number1-3
Publication statusPublished - 15-01-2000

Fingerprint

Matrix Theory
Annihilation
Completion
Closed-form
Product rule
Sweep
Elimination
Integer

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Cite this

Hartwig, Robert E. ; Prasad, K. M. / Creation and annihilation in matrix theory. In: Linear Algebra and Its Applications. 2000 ; Vol. 305, No. 1-3. pp. 47-65.
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Creation and annihilation in matrix theory. / Hartwig, Robert E.; Prasad, K. M.

In: Linear Algebra and Its Applications, Vol. 305, No. 1-3, 15.01.2000, p. 47-65.

Research output: Contribution to journalArticle

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