Dot products turn pairs of vectors into exact integers. The dot table shows the source vectors, a term-by-term walkthrough, and the resulting alignment scores.
highlighted = computed this step
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 alignment score under this chosen rule.
u⋅v=u1v1+u2v2
Term by term
The dot of cat=(3,1) with kitten=(2,1) is built one product at a time: 3 times 2 is 6, then 1 times 1 is 1. The running total goes 6 then 7, so cat dot kitten = 7, matching the dot table.
cat⋅kitten=3⋅2+1⋅1=6+1=7
Three exact dots
The exact dots are cat dot kitten = 7, cat dot car = 6, and kitten dot car = 5. These are scores from the assigned coordinate geometry.
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 integer dots for an argmax.