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Dot products and duality | Chapter 9, Essence of linear algebra

A 14-minute video by 3Blue1Brown about algebra and geometry, on the Mathematics shelf. It came up in r/3Blue1Brown, in a thread called “More 3Blue1Brown video suggestions”. It is pitched at introductory level.

3Blue1Brown, Video, 14 min, 2016, on the Mathematics shelf

Why the formula for dot products matches their geometric intuition.

Study notes

Introductory, Visual intuition. Step 1 of 13 in The mathematics of change and signals

Helpful first

• Vectors
• Coordinates

What it builds

• Relate a dot product to projection.
• Understand dot products through linear transformations.
• Connect vectors with their dual transformations.

Useful moments

• 0:34Why transformations matter
• 1:30Dot products as projection
• 4:13Duality

Check yourself: How can a dot product describe a projection without measuring an angle directly?

Next in the path: Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra

Notes are based on metadata, Reddit context and selected English caption passages. They are not a review of every claim in the video.