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.
Things people say
No one, and let me repeat that, no one “gets” linear algebra, differential equations, or frequency domain on the first pass. It takes years to absorb and multiple passes.
See:
Bruner / Spiral Curriculum.
Ebbinghaus / Spacing effect
Hattie / Deep-surface-transfer learning
Chunking (“How People Learn” has a good copy on this)
Etc.
The way you do this is you take a course, and then you take more courses. After a few years, it all connects and makes sense. The first course, I find, is often best short, simplified, and applied. Once you get through that, you can go deeper.
Different angles are nice too. For linear algebra:
Quantum computing
Statistics and probability
Machine learning
Control theory
Image processing
Abstract algebra / groups / etc.
Computer graphics
All come to mind.
On a mile-high level, this course seems ideal for a first pass. On a detailed level, I’m confused by some licensing issues.