Essence of Linear Algebra

[kurtbruns]

This pull request publishes the work in progress for bloggifying the rest of the linear algebra lessons:

• [ ] Preview | Chapter 0 Essence of linear algebra
  • [x] Phase 1
  • [ ] Phase 2
  • [ ] Phase 3
• [x] Vectors | Chapter 1 Essence of linear algebra*
• [x] Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra*
• [ ] Linear transformations and matrices | Chapter 3, Essence of linear algebra*
• [ ] Matrix multiplication as composition | Chapter 4, Essence of linear algebra*
• [ ] Three-dimensional linear transformations | Chapter 5, Essence of linear algebra
  • [x] Phase 1
  • [ ] Phase 2
  • [ ] Phase 3
• [ ] The determinant | Chapter 6, Essence of linear algebra*
• [ ] Inverse matrices, column space and null space | Chapter 7, Essence of linear algebra*
• [ ] Nonsquare matrices as transformations between dimensions | Chapter 8, Essence of linear algebra
  • [x] Phase 1
  • [ ] Phase 2
  • [ ] Phase 3
• [x] Dot products and duality | Chapter 9, Essence of linear algebra
  • [x] Phase 1
  • [x] Phase 2
  • [x] Phase 3
• [x] Cross products | Chapter 10, Essence of linear algebra
  • [x] Phase 1
  • [x] Phase 2
  • [x] Phase 3
• [x] Cross products in the light of linear transformations | Chapter 11, Essence of linear algebra
  • [x] Phase 1
  • [x] Phase 2
  • [x] Phase 3
• [ ] Cramer's rule, explained geometrically | Chapter 12, Essence of linear algebra
  • [x] Phase 1
  • [ ] Phase 2
  • [ ] Phase 3
• [ ] Change of basis | Chapter 13, Essence of linear algebra
  • [x] Phase 1
  • [ ] Phase 2
  • [ ] Phase 3
• [ ] Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra
  • [x] Phase 1
  • [ ] Phase 2
  • [ ] Phase 3
• [ ] A quick trick for computing eigenvalues | Chapter 15, Essence of linear algebra
  • [ ] Phase 1
  • [ ] Phase 2
  • [ ] Phase 3
• [ ] Abstract vector spaces | Chapter 16, Essence of linear algebra
  • [ ] Phase 1
  • [ ] Phase 2
  • [ ] Phase 3

*Text adaptation by River Way

Description of phases:

1. The MVP blog post. Images can be screenshots, animation clips have been extracted (if necessary), and the transcript is formatted into readable paragraphs. There just has to be something portable to a website allowing someone to scroll through and learn the lesson.
2. 3+ comprehension questions have been added to the article.
3. Images have been vectorized, and the page could theoretically be turned into a pdf.

Lesson authoring peer review checklist:

• Includes authorship line: Text adaptation by [Name]
• The lesson has an informative/compelling description, fit for a preview on the home page.
• The lesson has no grammar/spelling errors
• The lesson has no mathematical errors
• The table of contents effectively conveys the overall structure of the lesson
• The lesson uses no # Top Level headings
• The lesson includes well-chosen comprehension questions
• The lesson incorporates the core visuals from the video
• The visuals are clear and helpful for understanding
• The components are used in the places and ways they are intended (see the readme)

High-level notes:

• The moving camera in 3D scenes makes the before and after comparison of a transformation tricky.
• What is the priority of interactive vs. animation vs. textbook output (printable)?
• Light/dark theming
• Does it make sense to leave the original grid from a transformation in place when transformations are introduced, but then drop the convention later in the series?