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Module 1 · 3 lessons · about 85 minutes

Vectors and the dot product

Vectors as arrows and as lists, linear combinations, the dot product in algebra and geometry, length, and cosine similarity between embeddings.

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Exercises
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  1. 1Arrows and lists25 min
  2. 2The dot productOne small operation, multiply matching entries and add them up, measures how much two vectors point the same way. It is the most used calculation in machine learning.30 min
  3. 3Length and similarity30 min

Practice sets for this module

Fresh problems every time. Use them until the mechanics feel automatic.

Practice setDot product reps
3 correct in a row completes the set.

Compute a⋅b\mathbf{a}\cdot\mathbf{b} for a=(6,1)\mathbf{a} = (6, 1) and b=(−3,5)\mathbf{b} = (-3, 5).

a · b
Next moduleMatrices are machines