Let O(f) be the orthogonal
group of a symmetric bilinear form f defined on a finite-dimensional real vector space
V . If f is indefinite then O(f) has two conjugacy classes of reflections, one of which
consists of so called positive reflections. We denote by G+ the subgroup of O(f)
generated by all positive reflections. In this paper we describe this subgroup
and solve the length problem in G+ with respect to the distinguished set of
generators. When f is non-degenerate this problem was solved by J. Malzan. Our
proof (in the case of arbitrary f) is shorter and completely different from his
proof.
