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?
The other evening, trying to sleep, I picked up an unpublished 47-page 1993 paper, where Theorems 12 and 13 derive complicated trigonometric epxressions for the optimally compacting such "lapped" transforms. But it took a while to prove the Theorem 1 I'd proven 20 years earlier, and asked for in this thread. The only hint the paper gave was "From the definition we easily derive the following theorem." ::whack::