
Re: Nx2N lapped orthogonal transform
Posted:
Sep 3, 2013 6:06 PM


On Tue, 03 Sep 2013 16:51:42 +0100, Robin Chapman <R.J.Chapman@ex.ac.uk> wrote:
>On 03/09/2013 10:32, James Dow Allen wrote: >> James Dow Allen <gmail@jamesdowallen.nospam> might have writ, in >> news:XnsA22175B33BFDDjamesdowallen@178.63.61.175: >> >>> Let >>> ( A B 0 ) >>> ( 0 A B ) >>> ( B 0 A ) >>> be a 3Nx3N real matrix with A,B,0 each NxN and 0 an allzeros 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?) >> >> James Dow Allen <gmail@jamesdowallen.nospam> might have writ, in >> news:XnsA2236C8E3E26Ajamesdowallen@178.63.61.175: >> >>> I found it fruitful to introduce M = A + B; S = A  B > >Both orthogonal, of course. So what about MS^{1} = MS^t? >What can one say about that ... ?
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.
Leon

