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I mean have it been studied, does it have a name?

Like Transpose, Inverse, etc.. have names.

I wonder if the "inversion" of the components position have a name so then I could search material on this topic.

Thanks

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    @Apprentice Queue That seems to be the name! but it's seems not very popular..well is a good start, thanks. Srivatsan Narayanan I think reverse identity matrix fit best, thanks anyway2011-09-13

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I do not know anything about reversal specifically, but it is a special case of what is known as a permutation matrix.

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    As @ApprenticeQueue points out in $a$ comment, it is also sometimes called a reverse identity matrix. I found at least one reference that uses this term: http://www.wellesleycambridge.com/websections/cse11.pdf.2011-09-13