Vectors, matrices and the dot product

In ML, one data point is a vector, which is just a list of numbers. A house with area 120, 3 bedrooms and age 15 becomes [120, 3, 15]. A whole dataset is a matrix: one row per example and one column per feature.

The dot product multiplies two vectors item by item and adds up the results, so [1, 2, 3] · [4, 5, 6] = 4 + 10 + 18 = 32. It is the most important operation in this roadmap. A linear model's prediction is the dot product of its weights and the features.

Cosine similarity, used to compare embeddings (lists of numbers that stand for words or items), is a dot product after scaling both vectors to length 1. Learn the picture too: a large positive dot product means the vectors point the same way, and zero means they are at right angles.