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- W2031923905 abstract "Let F be a division ring and AϵGLn(F). We determine the smallest integer k such that A admits a factorization A=R1R2⋯Rk−1B, where R1,…,Rk−1 are reflections and B is such that rank(B−In)=1. We find that, apart from two very special exceptional cases, k=rank(A−In). In the exceptional cases k is one larger than this rank. The first exceptional case is the matrices A of the form Im⊕αIn−m where n−m⩾2, α≠−1, and α belongs to the center of F. The second exceptional case is the matrices A satisfying (A−In)2=0, rank(A−In)⩾2 in the case when char F≠2 only. This result is used to determine, in the case when F is commutative, the length of a matrix AϵGLn(F) with detA=±1 with respect to the set of all reflections in GLn(F)." @default.
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- W2031923905 date "1979-12-01" @default.
- W2031923905 modified "2023-09-28" @default.
- W2031923905 title "Products of reflections in the general linear group over a division ring" @default.
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- W2031923905 doi "https://doi.org/10.1016/0024-3795(79)90118-6" @default.
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