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

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Leon Aigret

Posts: 31
Registered: 12/2/12
Re: Nx2N lapped orthogonal transform
Posted: Sep 3, 2013 6:06 PM
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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 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?)

>>
>> 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



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