Dot products turn pairs of vectors into exact integers. The dot table shows the source vectors and recomputes each value from those integers.
The dot product
For two-dimensional vectors, u dot v is u1 times v1 plus u2 times v2. Because the coordinates are integers, the dot product is an integer.
u⋅v=u1v1+u2v2
Three exact dots
The exact dots are cat dot kitten = 7, cat dot car = 6, and kitten dot car = 5.
cat⋅kitten=7,cat⋅car=6,kitten⋅car=5
Summary
The dot table is self-contained: it shows the source vectors and recomputes every dot from them. The next lesson uses those dots for an exact argmax.
dots 7,6,5