Linear Algebra

This is an overview of the concepts I have learned during my linear algebra courses.

Courses

• Linear I at Marianopolis College notes here (Fall 2020)
• Linear II at Marianopolis College notes here (Winter 2021)
• Link to course notes (MATH115) here (Fall 2021, 1A SE)

On Linear Algebra

2025-01-18: Although I took linear algebra 3 times (2 in high school, 1x in college), I don’t think I’d be able to explain very deeply intuitions behind linear algebra. I know how to apply formulas (but so can anyone)…

I am restudying linear algebra, as I want to break more into AI research, and that requires a very very deep understanding of LA and statistics.

Voted:

• https://www.reddit.com/r/math/comments/17jbek7/best_linear_algebra_textbook_for_someone_who/

https://link-springer-com.proxy.lib.uwaterloo.ca/content/pdf/10.1007/978-3-031-41026-0.pdf

Concepts

• Complex Number
• Vector
• Line
• Plane
• Projection
• Linear Combination Sets and Spans
• Linear Independence
• Subspace
• Matrix
• Markov Chain
• Linear Transformation
• Eigenvalues and Eigenvectors
• Vector Space

Final Exam Gaps in Knowledge

Whenever you find the basis, at the end, you have to say that the nonzero vectors in the spanning set are linearly independent.

• Main focus is lecture 20 onwards
• Complex Nth Roots p.20
• System-Rank Theorem, how many solutions (Lecture 21)
• Applications of Linear Algebra (Lecture 23)
• Fundamental Subspaces (Null, Row, Col) Lecture 27
  • Find the row space etc.

Related and Applications

• Make a video on this
• #todo
• • Linear Models
  • Balancing Chemical Equations
  • Network Flow
  • Electrical Networks