### 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 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

Hartwig, R. E., & Prasad, K. M. (2000). Creation and annihilation in matrix theory.

*Linear Algebra and Its Applications*,*305*(1-3), 47-65.