Lilly Tech Systems
Linear Algebra for AI
Master the mathematical foundation that powers modern machine learning. From vectors and matrices to eigenvalues and SVD, learn the linear algebra concepts essential for understanding neural networks, dimensionality reduction, and data transformations.
What You'll Learn
By the end of this course, you'll understand the linear algebra foundations that drive AI and machine learning algorithms.
Vectors & Spaces
Understand vector operations, dot products, norms, and vector spaces that form the language of data representation in ML.
Matrix Operations
Master matrix multiplication, inverses, determinants, and transformations used throughout deep learning.
Eigenvalues & SVD
Learn eigendecomposition and singular value decomposition for PCA, recommendation systems, and data compression.
ML Applications
See how linear algebra connects to real ML tasks: neural network layers, image processing, and NLP embeddings.
Course Lessons
Follow the lessons in order or jump to any topic you need.
1. Introduction
Why linear algebra matters for AI. Overview of the mathematical landscape and how it connects to machine learning concepts.
2. Vectors
Vector operations, dot products, cross products, norms, and vector spaces. The building blocks of data representation.
3. Matrices
Matrix operations, multiplication, inverses, determinants, rank, and linear transformations in machine learning.
4. Eigenvalues
Eigenvalues, eigenvectors, eigendecomposition, and their critical role in PCA and spectral methods.
5. SVD
Singular Value Decomposition: theory, computation, and applications in dimensionality reduction and recommender systems.
6. Applications in ML
Real-world applications: neural network weight matrices, image processing, NLP word embeddings, and data pipelines.
7. Best Practices
Numerical stability, computational efficiency, library usage (NumPy, PyTorch), and common pitfalls to avoid.
Prerequisites
What you need before starting this course.
- Basic understanding of algebra and arithmetic
- Familiarity with Python (for code examples)
- NumPy installed for hands-on exercises
- Curiosity about how math powers AI systems