tags : Math

## Products

Inner product and Outer product are terms from “Geometric Algebra”

### Inner product

works on abstract vector spaces

#### Dot Product / Scalar product

- Intuition
- “the amount that two vectors are pushing in the same direction.”
- Dot products and duality | Chapter 9, Essence of linear algebra - YouTube

- Use
- Way of turning two vectors into a number in a way that respects how long each vector is and how much the vectors overlap.
- Can serve as a measure of how similar two vectors are.

- Eg.
- work is the dot product of force and displacement.
- power is the dot product of force and velocity.

### Outer product

#### Cross product

### Wedge product

- In differential topology, it works on differential forms and antisymmetrizes them to make a higher degree differential form.