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 $\endgroup$– HenryJun 26, 2015 at 13:43
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$\begingroup$ @Henry it it also called exchange matrix: en.wikipedia.org/wiki/Exchange_matrix $\endgroup$– lisyarusJun 26, 2015 at 13:54
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1 Answer
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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, 2015 at 13:42
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2$\begingroup$ Your matrix is not an operator ? $\endgroup$– user42761Jun 26, 2015 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. $\endgroup$ Jun 26, 2015 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. $\endgroup$ Jun 26, 2015 at 13:49