kamilkrawczyk.dev

Appearance

Linear Algebra ​

Course Overview ​

University: MIT
Course Code: 18.06SC
Instructor: Gilbert Strang
Status: Not Started
Progress: 0/35 lectures

The language of data. Non-negotiable for AI and machine learning. This course will fundamentally change how you think about matrices and vectors.

Resources ​

📚 MIT 18.06SC OpenCourseWare
📺 Video Lectures
📖 Textbook: Introduction to Linear Algebra by Gilbert Strang

Key Topics ​

Part 1: Vectors and Matrices ​

  • Vectors and matrices
  • Matrix multiplication
  • Inverses and transposes
  • Orthogonal matrices

Part 2: Solving Linear Systems ​

  • Gaussian elimination
  • Matrix factorization (LU)
  • Forward and back substitution

Part 3: Vector Spaces ​

  • Column space and null space
  • Rank and dimension
  • Linear independence and bases
  • Orthogonal vectors and projections

Part 4: Eigenvalues and Eigenvectors ​

  • Characteristic polynomial
  • Finding eigenvalues and eigenvectors
  • Diagonalization
  • Applications to dynamical systems

Part 5: Applications ​

  • Least squares
  • Principal Component Analysis (PCA)
  • Singular Value Decomposition (SVD)
  • Applications in data science

Why This Matters ​

Linear algebra is everywhere in machine learning:

  • Neural networks: Weights are matrices, activations are vectors
  • Optimization: Gradients and Hessians
  • Data analysis: PCA, SVD for dimensionality reduction
  • Transformations: Rotations, projections, scaling

Learning Goals ​

By the end of this course, you should be able to:

  • Perform matrix operations fluently
  • Solve systems of linear equations
  • Understand vector spaces and subspaces
  • Find and interpret eigenvalues and eigenvectors
  • Apply linear algebra to real-world problems
  • Understand the geometry of linear transformations

Study Plan ​

Estimated Time: 6-8 hours/week for 12-14 weeks

  • Lectures: ~3 hours/week
  • Problem Sets: ~3-4 hours/week
  • Exams: ~1-2 hours/week (practice)

Daily Notes ​

Lecture 1-4: Introduction ​

  • [ ] Lecture 1: The Geometry of Linear Equations
  • [ ] Lecture 2: Elimination with Matrices
  • [ ] Lecture 3: Multiplication and Inverse Matrices
  • [ ] Lecture 4: Factorization into A=LU

Problem Sets ​

Key Concepts & Formulas ​

Intuitive Understanding ​

Key Takeaways ​

← Previous: Calculus 2 | [← Back to Winter Quarter](Online Studying/CS - Stanford, MIT, Berkley/Year 1/Winter Quarter/index)