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

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 Nicolas Bonneel Posts: 6 Registered: 4/23/13
Re: Nx2N lapped orthogonal transform
Posted: Aug 20, 2013 4:03 PM
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On 8/20/2013 3:42 PM, quasi wrote:
> Nicolas Bonneel wrote:
>> Robin Chapman wrote:
>>> Nicolas Bonneel wrote:
>>>> James Dow Allen wrote:
>>>>>
>>>>> 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?

>>>>
>>>> by direct computation, AB=BA=0 and A^2+B^2=Id, right?

>>>
>>> No

>>
>> ok, but why not ?
>>
>> Noting the matrix above M, I just did M^T.M=Id and directly
>> computed the matrix multiplication per block.

>
> You didn't do the transpose correctly.
>
> The inner blocks need to get transposed as well.

ouch, indeed! :)

--
Nicolas Bonneel

Date Subject Author
8/19/13 James Dow Allen
8/19/13 Nicolas Bonneel
8/20/13 Robin Chapman
8/20/13 Nicolas Bonneel
8/20/13 quasi
8/20/13 Nicolas Bonneel
8/20/13 Roland Franzius
8/20/13 James Dow Allen
9/3/13 James Dow Allen
9/3/13 Robin Chapman
9/3/13 Leon Aigret
9/5/13 James Dow Allen
9/5/13 Robin Chapman
9/12/13 Leon Aigret

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