Products of reflections in the general linear group over a division ring

@inproceedings{Djokovi1979ProductsOR,
  title={Products of reflections in the general linear group over a division ring},
  author={Dragomir Z. Djokovi{\'c} and Jerry Malzan},
  year={1979}
}
Abstract Let F be a division ring and Aϵ GL n ( F ). We determine the smallest integer k such that A admits a factorization A = R 1 R 2 ⋯ R k −1 B , where R 1 ,…, R k −1 are reflections and B is such that rank( B − I n )=1. We find that, apart from two very special exceptional cases, k =rank( A − I n ). In the exceptional cases k is one larger than this rank. The first exceptional case is the matrices A of the form I m ⊕ αI n − m where n − m ⩾2, α ≠−1, and α belongs to the center of F . The… CONTINUE READING