### 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 language | English |
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Pages (from-to) | 47-65 |

Number of pages | 19 |

Journal | Linear Algebra and Its Applications |

Volume | 305 |

Issue number | 1-3 |

Publication status | Published - 15-01-2000 |

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### All Science Journal Classification (ASJC) codes

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

### Cite this

*Linear Algebra and Its Applications*,

*305*(1-3), 47-65.

}

*Linear Algebra and Its Applications*, vol. 305, no. 1-3, pp. 47-65.

**Creation and annihilation in matrix theory.** / Hartwig, Robert E.; Prasad, K. M.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Creation and annihilation in matrix theory

AU - Hartwig, Robert E.

AU - Prasad, K. M.

PY - 2000/1/15

Y1 - 2000/1/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0034400895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034400895&partnerID=8YFLogxK

M3 - Article

VL - 305

SP - 47

EP - 65

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 1-3

ER -