'Interesting' orthogonal martices?
I'm working with an algorithm that takes as part of its input an
orthogonal matrix with real entries. I'm trying to understand how the
specification of this matrix affects performance of the algorithm. It's
very difficult to do this analytically, so I'm working experimentally for
now.
I'm loking for examples of orthogonal matrices that are in some sense
'interesting' or 'extreme'. Obviously the identity matrix is one choice.
Another choice might be the matrix that is 'least sparse' in the sense
that the sum of the absolute values of the entries is as large as possible
(is there a name for this?). Another choice is a random sample from the
Gaussian orthogonal ensemble.
Can anyone suggest some other examples?
Many thanks.
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