A key concept, in the article, is that the dot product measures “similarity”. It measures similarity by only including the contribution of other vectors that are along a reference vector, as denoted by cos(theta). Another key concept is that the cross-product measures differences. Just like cos(theta) is associated with the dot product, the article suggests that sin(theta) is associated with the cross-product. Let’s recall that within a unit circle sin(theta) + cos(theta) = 1. If cos(theta) measure similarity, then 1- cos(theta) measures difference. 1 – cos(theta) = sin(theta). But as the article states, there are details missing if only sin(theta) is considered. Hopefully this makes explicit one of the article’s key conceptual building blocks.

A key concept, in the article, is that the dot product measure “similarity”. It measures similarity by only including the contribution of other vectors that are along a reference vector, as denoted by cos(theta). Another key concept is that the cross product measures difference. It does so because within a unit circle sin(theta) + cos(theta) = 1. If cos(theta) measure similarity, then 1- cos(theta) measures difference. 1 – cos(theta) = sin(theta). But as the article states, there are details missing if only sin(theta) is considered. Hopefully this makes explicit one of the articles key conceptual building blocks.