Date: Aug 19, 2013 12:34 AM
Author: James Dow Allen
Subject: Nx2N lapped orthogonal transform
Let

( A B 0 )

( 0 A B )

( B 0 A )

be a 3Nx3N real matrix with A,B,0 each NxN and 0 an all-zeros matrix.

What is the necessary and sufficient condition for that matrix to be

orthogonal, i.e. that its transpose also be its inverse?

This problem statement can be considered ambiguous.

*But if you derive a good parametric form for (A B) you will know it.*

(I already "know the answer." I post from curiosity: Is this a VERY easy

problem, or just an easy problem.)

The problem does have some historic interest. Such transforms were in

vogue, briefly(?), in the 1990's for signal compression. A certain

Computer Sci. Professor published several papers and even a full-length

textbook on Nx2N lapped orthogonal transforms, with numerous Remarks and

Theorems which would all have been trivial Corollaries had he solved the

problem posed above.

James Dow Allen