Products of similar matrices. (English) Zbl 0893.20033
The author shows, if \(A\) is a noncentral matrix in the special linear group \(\text{SL}_n(K)\), where \(n>2\) or \(| K|>3\), then every element in \(\text{SL}_n(K)\) is a product of matrices conjugate to \(A\). He gets similar results for the symplectic and for the special orthogonal groups, as well as for semisimple algebraic groups over local fields.
Reviewer: E.Ellers (Toronto)
MSC:
20G15 | Linear algebraic groups over arbitrary fields |
20G25 | Linear algebraic groups over local fields and their integers |
15A23 | Factorization of matrices |
20F05 | Generators, relations, and presentations of groups |