Linear Algebra
Dot Products Measure Agreement
8 min+70 XPStep 1/10
Multiply the pairs, add it up
The dot product is almost embarrassingly simple: multiply matching entries, then add the results. [1, 3] · [2, 4] = 1×2 + 3×4 = 14.
Why does this arithmetic measure geometry? Because the computation secretly equals (length of one arrow) × (how much of the other points along it). Agreement between directions falls straight out of the sum.
The result reads like a dial:
- Large positive → same direction, strong agreement
- Zero → perpendicular, no relationship at all
- Negative → pulling apart, opposing directions
insight
Perpendicular vectors have dot product zero — not 'opposite.' Opposite is negative. Zero means 'completely unrelated,' which in ML is its own kind of information.