Maths 2.3Lesson outlineLesson 3 of 5 in Module 2
The Dot Product, Angle and Projection
Compute a dot product and read it as alignment, and project one vector onto another.
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Learn
In this lesson10 parts
- 01Same words, different lengths
- 02The dot product
- 03The sign of the dot product
- 04The cosine and the angle between two vectors
- 05Unit vectors and projection
- 06Checkpoint: what the dot product measures
- 07Emails as vectors and cosine similarity
- 08When length matters
- 09The dot product, cosine and projection in NumPy
- 10Recap, challenge, and next: lines, planes and hyperplanes
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- dot product
- the sum of the products of matching components |
(3, 4) · (2, 1) = 10 - orthogonal
- perpendicular; dot product zero |
(3, 4)and(0.8, −0.6) - cosine
- the horizontal coordinate of the point at angle θ on the unit circle |
cos 60° = 0.5 - angle between vectors
cos θ = a · b / (‖a‖ ‖b‖)|26.57°- unit vector
- a vector of length one,
a / ‖a‖|(0.6, 0.8) - projection
- the part of a vector along a direction,
(b · â) â|(1.2, 1.6) - count vector
- one component per vocabulary word | email 12,
(2, 0, 1, 1, 1, 0, 0, 0, 0, 0) - cosine similarity
- the cosine of the angle between two vectors |
0.5714for emails 12 and 13
Quiz
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.