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

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Robin Chapman

Posts: 297
Registered: 5/29/08
Re: Nx2N lapped orthogonal transform
Posted: Sep 3, 2013 11:51 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 ... ?




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