Implementing Linear Algebra for Machine Learning from Scratch: A Six-Week Deep Dive Course

Title: Implementing Linear Algebra for Machine Learning from Scratch: A Six-Week Deep Dive Course Abstract: This open-source course teaches the linear algebra fundamentals required for machine learning from scratch using pure NumPy, helping learners truly understand the mathematical principles behind algorithms instead of just calling black-box functions. Original Author/Maintainer: HAYDARKILIC Source Platform: GitHub Original Link: https://github.com/HAYDARKILIC/linear_algebra_for_ml Publication Date: May 26, 2026

The core of this course is to use the "first principles" learning method, allowing learners to implement linear algebra algorithms by hand and build deep intuition for ML algorithms.

In machine learning practice, most developers rely on high-level APIs (e.g., np.linalg.inv()) to quickly build models, but this hides the mathematical essence. When models face convergence issues, numerical instability, or need optimization, the lack of low-level understanding becomes a bottleneck.

Course Design Philosophy: Before calling ready-made functions, you must implement and understand their principles by hand—this method helps build deep intuition.

The course is a six-week plan, with each week focusing on a core scenario:

1. Week 1: Basic operations of vectors and matrices (addition, scalar multiplication, geometric meaning of dot and cross products, implemented with pure NumPy)
2. Weeks 2-3: Core matrix operations (multiplication, transposition, inverse matrices; emphasizing computational complexity and optimization)
3. Weeks 4-5: Matrix decomposition techniques (LU/QR/SVD/eigenvalue decomposition; numerical stability and scenario selection)
4. Week 6: Integrate knowledge to implement linear regression, logistic regression, and gradient descent optimizers.

Choosing NumPy as the only dependency is a deliberate decision: it provides basic operations for multi-dimensional arrays but no high-level linear algebra functions, forcing learners to think about low-level details.

Examples: When implementing matrix multiplication, consider the impact of triple loop order on cache hit rate; handle numerical stability when the pivot is zero in Gaussian elimination; understand the convergence conditions of the power method for eigenvalue calculation.

After completing the implementations, you can understand the design principles of scientific computing libraries, such as complexity, numerical precision, and trade-offs in approximate algorithms.

The course deeply connects linear algebra concepts with ML models:

• Matrix inversion is a core step in the normal equation (least squares method)
• Eigenvalue decomposition is the theoretical foundation of PCA dimensionality reduction
• Gradient calculation is the mathematical essence of backpropagation in neural networks

This connection helps build a bridge between theory and practice, treating linear algebra as the core mechanism driving AI—critical for reading papers, debugging models, and designing algorithm architectures.

Target Groups:

1. Learners with programming basics who want to deeply understand the mathematical principles of ML (already able to build simple models using Python/scikit-learn)
2. Computer science students (as a supplement to linear algebra practice)
3. Experienced ML engineers (return to basics to rebuild a solid foundation).

Learning Suggestions:

• Allocate 10-15 hours per week (reading, coding, debugging); prioritize understanding over speed
• Use Jupyter Notebook for interactive learning to instantly verify the correctness of steps
• Use matplotlib to visualize the geometric effects of matrix transformations
• Community Contribution: Submit PRs to improve implementations, explanations, or fix bugs; collaborative learning deepens understanding.

This course helps cross the gap between 'package callers' and 'principle experts', turning you into an active designer who understands algorithm principles through six weeks of training.

Long-term Returns: Quickly understanding the mathematical foundations of new models, diagnosing numerical issues in production environments, and optimizing algorithm decisions—these are key abilities that distinguish ordinary developers from excellent engineers.