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Linear algebra 2

Multiply matching parts and add them up. That one calculation tells you how much two arrows agree, how long an arrow is, who has the most similar taste, what an order cost, and which side of a line a point is on — and it is the calculation underneath machine learning.

Briefing

One calculation runs through this whole lab: multiply matching parts and add them up. On a grid you watch it measure how much two arrows agree, how long one is, whose taste matches whose, and which side of a line a point falls on.

You'll learn to

  • Compute a dot product and read its sign as agreement
  • Find a vector's length, and the most similar of several
  • Use it to price an order and to test for a right angle
  • Split points with a line — the calculation under machine learning
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Start: Multiply and add
Before the dot productOptional warm-upMultiplying matching parts, right angles, Pythagoras, and why "similar" means "pointing the same way". Ten minutes.

  1. Multiply and add

    Up next

    What the dot product is, and what its sign means

  2. How long is an arrow?

    Length is an arrow dotted with itself

  3. Closest match

    Direction, not size

  4. Two receipts

    A matrix is several dot products at once

  5. Your first classifier

    A score, a line, and a decision

  6. Where dot products live

    Search, recommendations and AI