Module 2: Linear Algebra

Goal

Understand how AI systems represent data and transform information using vectors, matrices, and geometric intuition.

This module focuses on the mathematical language used throughout machine learning: vectors for representing data, matrices for transforming features, and dot products for measuring similarity.

Estimated Time Impact

60-70 hours total

Linear Algebra(60h)

1. Primary Resources

course

beginner

Linear Algebra - Khan Academy

10-12 hours

Additional Resources

video

beginner

Essence of Linear Algebra - 3Blue1Brown

6-8 hours

Why it matters:

AI models operate on numerical representations.

• Vectors represent inputs such as text embeddings, image pixels, audio features, and user behavior.
• Matrices transform those representations through layers, projections, and feature combinations.
• Dot products measure alignment and similarity, which appears in retrieval, attention, recommendation, and classification systems.

Without linear algebra, AI systems remain a black box. With it, you can reason about what models store, compare, and transform.

This module connects abstract math to concrete AI behavior.

What to expect:

By the end of this module, learners will:

• Understand vectors as representations of data
• Interpret matrix multiplication as transformation and combination of features
• Build intuition for dot products as a measure of similarity
• Understand how high-dimensional representations appear in modern AI systems
• Connect linear algebra concepts to embeddings, neural network layers, and similarity search

After completing this module, learners will understand how AI models represent and transform information.

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Completion Checklist

• Completed core units in Linear Algebra - Khan Academy (vectors, matrices, matrix multiplication, linear transformations), with a final exam score ≥ 80%.
• Watched Essence of Linear Algebra - 3Blue1Brown and wrote short notes connecting vectors, matrices, and dot products to AI systems.