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.