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Course

Linear Algebra for Machine Learning

Foundational linear algebra — vectors, matrix transformations, eigenvalues, eigenvectors, and SVD — through high-impact 2D/3D motion graphics and hands-on Python/NumPy applications.

4.3
Created by Prof. Julian HayesLast updated 7/2026English

What you'll learn

Grasp core linear algebra concepts through step-by-step 2D and 3D motion graphics
Visualize vectors, linear combinations, span, and basis vectors geometrically
Understand matrices as spatial transformations (scaling, rotation, reflection, shearing)
Master matrix multiplication, determinants, and systems of linear equations
Explore vector spaces, subspaces, null space, and column space
Master dot products, cross products, projections, and orthogonalization
Calculate and geometrically interpret eigenvalues, eigenvectors, and eigenspaces
Deconstruct Singular Value Decomposition (SVD) and Principal Component Analysis (PCA)
Implement linear algebra concepts in Python using NumPy and SciPy
Apply linear algebra directly to computer graphics, machine learning, and data science

This course includes

  • 2 hours on-demand video
  • 22 articles
  • 42 downloadable resources
  • Access on mobile and TV
  • Closed captions
  • Certificate of completion
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From $99/year

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Course content

4 sections
01

Matrix Fundamentals

Builds the core vocabulary of matrices — vector norms, matrix rank, and the identity matrix — as the foundation for everything that follows.

3 lessonsQuizNotebook
02

Advanced Matrices & Decomposition

Covers symmetric and positive definite matrices, rotation and reflection matrices, orthogonal matrices, and LU decomposition of triangular matrices.

4 lessonsQuizNotebook
03

Calculus & Eigen Theory

Connects calculus to linear algebra through eigenvalues and eigenvectors, matrix derivatives, the Jacobian, and the Hessian.

4 lessonsQuizNotebook
04

Data Science Applications

Applies the theory directly to data science — PCA as eigenvectors of the covariance matrix, and cosine similarity as a measure of direction.

2 lessonsQuizNotebook

Requirements

  • High school algebra (basic coordinate planes and simple equations)
  • Basic familiarity with Python is helpful for coding sections, but not required
  • No prior university-level math or linear algebra experience necessary
  • A drive to build visual intuition for how math powers modern technology
Secret Sauce

Why this course works

Description

Are you aspiring to work as a Data Scientist, Machine Learning Engineer, AI Specialist, Game Developer, or Quantitative Analyst? Do you want to build an intuitive, visual understanding of linear algebra without getting buried in dry, mechanical matrix arithmetic and static equations?

Linear Algebra, Visualized is designed specifically to make abstract mathematical structures crystal clear through custom 2D and 3D motion graphics, rich animations, and practical NumPy implementations. Instead of treating matrices as arbitrary grids of numbers, every lesson uses fully animated motion graphics to show you exactly how matrices transform space, why determinants measure area and volume scaling, and how eigenvectors stay on their span during transformations.

Fully animatedHighly intuitiveFully comprehensiveDirect and conciseGrounded in Python & NumPyRich in hands-on notebooksBuilt on spatial intuition

Linear algebra is taught in universities worldwide, but a structured program that clearly and visually explains the geometric reasoning behind these operations is rare. Modern libraries handle the computation instantly — this course equips you with something far more essential: true mathematical intuition. We spent months of full-time development crafting custom motion graphics and 3D render pipelines, so your enrollment includes animated visual walkthroughs, structured Jupyter notebooks, practice problem sets, and downloadable cheat sheets.

What sets this course apart

Custom Motion Graphics

100% animated visual lessons that transform abstract equations into clear, memorable spatial concepts.

Expert Instruction

Led by an experienced mathematician and computer science instructor.

Complete Curriculum

Covers every linear algebra topic needed for modern AI, data science, and graphics engineering.

Practical Code

Hands-on Python and NumPy notebooks alongside every visual breakdown.

Responsive Support

Get answers to your technical questions within one business day.

Efficient Pacing

Tightly edited, zero-fluff lessons designed to maximize learning speed.

Why master these skills

The Engine of Modern AI

Linear algebra is the core mathematical foundation powering neural networks, computer vision, and modern ML.

Career Advancement

Deep spatial intuition for transformations sets top-tier technical professionals apart.

Future-Proof Skills

Frameworks change constantly; the geometric principles of linear algebra remain timeless.

Universal Application

From rendering 3D graphics to reducing dataset dimensionality, linear algebra is everywhere.

This course is backed by Otomas' 30-day money-back guarantee, giving you a risk-free opportunity to explore the material.

Who this course is for

  • Individuals pursuing a career in Machine Learning, AI, Data Science, or Computer Graphics
  • Software Engineers wanting to understand the math behind modern algorithms
  • Computer Science and Math students looking for a visual supplement to lectures
  • Game Developers working with 3D transformations, physics, and rendering
  • Visual learners who find traditional, symbol-heavy math lectures dry or abstract
  • Anyone looking to build a rock-solid, visual foundation in Linear Algebra
4.3 course rating