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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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