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

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quasi

Posts: 10,396
Registered: 7/15/05
Re: Nx2N lapped orthogonal transform
Posted: Aug 20, 2013 2:57 PM
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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.

quasi



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