On 05/09/2013 12:00, James Dow Allen wrote: > Leon Aigret <email@example.com> might have writ, in > news:firstname.lastname@example.org: > >> The AB^t = 0 condition translates to the requirement that MS^t is both >> its own transpose and its own inverse, with drastic consequences for >> its eigenvectors and eigenvalues. > > This is the essential point, and leads directly to the unique parametric > form I sought. Do such matrixes, which are both symmetric and orthogonal, > arise often?
They correspond to vector subspaces of R^n. For such a subspace V it acts as +1 on V and -1 on the orthogonal complement of V.