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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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    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".2011-09-13
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    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".2011-09-13
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    you are right, I will edit, thanks2011-09-13
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    Well if a single vector is an ordered set, yes, is an ordered set, but is there any "known" operation for that order reversion? for example determinant of matrix A, could be noted as det(A), and there are a lot of application of determinant, like inversion, convolution, etc.. thanks for "reverse order" keyword, I find a *fliplr* command for matlab, but I still wonder about a "math name"2011-09-13
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    Reversal is a standard operation for [strings](http://en.wikipedia.org/wiki/String_(computer_science)). It is not commonly used in the context of vectors, but I do not see any harm in using it (after you define it explicitly, of course). ADDED: Reg. finding references, I do not think reversal will be much help, but you can try it for yourself.2011-09-13
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    @Srivatsan Narayanan Just asking to avoid reinvent the wheel, imagine if the operation I were looking is "determinant", then I would waste time in "define it explicitly" (if I can), and of course I would lost the huge literature over that.. well if it's "more for strings", I agree I should use my own notation2011-09-13
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    It's the called the reverse identity matrix J. J[1 2 3 4]^T = [4 3 2 1]^T.2011-09-13
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    Ok, I will tell you what I know about strings; you can use it if you like it. The operation (standard in this context) is called string reverse or string reversal. It is notated by an $R$ in superscript: like, $w^R$ where $w$ is the string.2011-09-13
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    @Appren Why don't you post your comment as an answer? (May be you could add some reference for the term.)2011-09-13
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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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    Specifically, the permutation matrix for this operation is termed as an [exchange matrix](http://en.wikipedia.org/wiki/Exchange_matrix).2011-09-13
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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