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How I generate all possible pairs of matrices?

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Ammy
Ammy 2018-1-26
关闭： Walter Roberson 2018-1-26
First I define orthogonal matrix as when I combine two matrices (entry in first matrix with the corresponding entry in second matrix) there is no repetition in the ordered pair in the whole new matrix . e.g
A=[1 2 3;2 3 1; 3 2 1] and B=[1 2 3;3 1 2;2 1 3]
New = [1 1 2 2 3 3; 2 3 3 1 1 2; 3 2 2 1 1 3]
In the resulting matrix there is no repetition in the pairs.
If I have 120 such matrices , how I generate all possible mutually orthogonal out of these 120.

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Ammy
Ammy 2018-1-26
The question is same as earlier , but still I don't know the appropriate way to get all possible pairs in MATLAB. Would you please like to introduce any code that solve my problem.

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