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Topic: Nx2N lapped orthogonal transform
Replies: 13   Last Post: Sep 12, 2013 7:38 PM

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James Dow Allen

Posts: 15
Registered: 12/14/08
Re: Nx2N lapped orthogonal transform
Posted: Sep 5, 2013 7:00 AM
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Leon Aigret <aigret.not@myrealbox.invalid> might have writ, in
news:vsmc29lmof1ah5npckgve85u0rp2sjuh0o@4ax.com:

> 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The other evening, trying to sleep, I picked up an unpublished 47-page 1993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::

James



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