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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.


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Are you talking about infinite vectors here? Because I don't understand why you'd want to consider a vector which does have a "bottom" but no "top". – TMM Sep 13 '11 at 19:28
If you think of $[1,2,3,4,\ldots]$ as an ordered set (as opposed to a vector), then $[\ldots,4,3,2,1]$ is the set in the "reverse order". – Arturo Magidin Sep 13 '11 at 19:29
you are right, I will edit, thanks – Hernán Eche Sep 13 '11 at 19:29
It's the called the reverse identity matrix J. J[1 2 3 4]^T = [4 3 2 1]^T. – Apprentice Queue Sep 13 '11 at 19:41
@Appren Why don't you post your comment as an answer? (May be you could add some reference for the term.) – Srivatsan Sep 13 '11 at 19:51
up vote 4 down vote accepted

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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+1 I think yes. – Hernán Eche Sep 13 '11 at 21:46
Specifically, the permutation matrix for this operation is termed as an exchange matrix. – J. M. Sep 13 '11 at 23:49
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: – Srivatsan Sep 13 '11 at 23:54

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