Products of Transvections

Abstract

This paper is concerned with the presentation of certain elements of the groupSL(n,K) as products of a minimal number of transvections. To explain the terminology, letVbe ann-dimensional left vector space over a (not necessarily commutative) fieldK. The group of all non-singular linear transformations ofVontoV(i.e. the group of all collineations ofV) is the groupGL(n,K). This group is generated by collineations leaving a hyperplane pointwise fixed. Whenn= 2 these collineations are called axial collineations and the invariant hyperplane (line) is then called an axis.