Is the dot product a symmetric or anti-symmetric operator?

Question

To me it is clearly symmetric but I'm finding "the dot product is an anti-symmetric operator" in the following paper: https://arxiv.org/abs/1607.03780 I'm not sure I properly understand what the authors are trying to convey. Any idea?

Answer 1

Here's the relevant excerpt (which you should have provided):

Two words are predicted to be similar if the dot product between their vectors is high. But the dot product is an anti-symmetric operator, which makes it more natural to interpret these vectors as representing whether features are true or false, whereas the dichotomy known versus unknown is asymmetric.

Your question is reasonable. The dot product is indeed symmetric - its value is unchanged when you switch the arguments. I suspect from the context that the authors are writing about vectors of unit length and mean to call attention to the fact that $(-A) \cdot B = -(A \cdot B)$ . Whether that interpretation makes sense depends on understanding the context more than I care to take the time to try.