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 |
|---|---|
| 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