Is there a mathematical operator which flips a vector from left to right (or up to down). Say \begin{align} a = [1~ 2~ 3]\quad\text{and}\quad b = [3~ 2~ 1] \end{align} I'd like to have \begin{align} a = \sigma\circ b \end{align} where $\sigma$ is the flip operator. How would you define it? Or does the operator might exists already and I'm just not aware?
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1$\begingroup$ Multiply it by an anti-diagonal unit matrix $\endgroup$ – Henry Jun 26 '15 at 13:43
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$\begingroup$ @Henry it it also called exchange matrix: en.wikipedia.org/wiki/Exchange_matrix $\endgroup$ – lisyarus Jun 26 '15 at 13:54
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I don't know of any such operator, however, you could multiply your vector by the matrix
$\begin{bmatrix} 0 & 0 &1 \\ 0& 1 &0 \\ 1&0 &0 \end{bmatrix}$
and then take the transpose.
answered Jun 26 '15 at 13:42
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2$\begingroup$ Your matrix is not an operator ? $\endgroup$ – user42761 Jun 26 '15 at 13:45
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$\begingroup$ No. In fact, I don't know of any operator that will work, I was just trying to helpful and my reputation score isn't high enough to just post a comment yet. $\endgroup$ – man_in_green_shirt Jun 26 '15 at 13:46
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1$\begingroup$ @someone: Your matrix may not be an operator, but it certainly corresponds to one. In this context, the term "operator" is simply another word for "linear transformation" between two vector spaces, and left multiplication with your matrix defines such an operator. $\endgroup$ – hmakholm left over Monica Jun 26 '15 at 13:49
