The mathematics inside the models
Know what vectors, matrices, projections and factorizations are doing inside machine learning and AI models, so you can read the papers and code built on them and judge them for yourself.
Partners and press
Overview
The language underneath machine learning and AI.
An intensive course that takes you from vectors and matrices to projections, factorization and SVD, with every idea tied to the data science, machine learning and AI it powers.
Students and professionals alike come away with a deep conceptual command of the subject, and the practical skill to apply it to real problems.
80Hours
6Modules
4.9Rating
10,000+Students
What you’ll learn
Learn all the way down.
Learn all the way down.
Perform when it matters.
Deep conceptual understanding
A robust grasp of the fundamentals and the advanced topics, so you can take on complex mathematical problems and sharpen the way you think about them.
Skills the field asks for
Mathematics in high demand across technology and engineering, especially machine learning and AI, and the kind that makes you the person others turn to.
Practical application
Apply linear algebra directly to real scenarios in data science, machine learning and AI, improving how you develop algorithms and solve technical challenges.
Course outline
Six modules, from the
Six modules, from the
first vector to SVD.
This module reinforces essential prerequisites like real numbers, vector norms and geometric basics using the Cartesian coordinate system, setting a strong foundation for advanced linear algebra applications, as well as the Linear Algebra RoadMap for 2024.
This module goes deep into vector operations, covering fundamental concepts, special vectors, and operations such as dot products and the Cauchy–Schwarz inequality, linear combinations, and geometric intuition and interpretation, with an emphasis on applications in machine learning and analytical geometry.
This module introduces the foundational concepts of matrices, including their types and structures, and basic operations such as addition, subtraction and scalar multiplication, as well as matrix multiplication, essential for more complex algebraic manipulation.
This module covers advanced techniques like Gaussian elimination, REF and RREF (reduced row echelon forms), and the applications of matrices in solving linear systems, null space, column space, basis and rank, emphasizing critical thinking and problem-solving in algebra.
This module dives into the matrix determinant, inverses and transpose operations, detailing methods for calculating inverses of 2×2 and 3×3 matrices and their practical applications, while explaining the significance of these transformations in relation to the dot product and matrix functionality.
This unit explores sophisticated concepts in vector spaces and matrix operations, including projections, the Gram–Schmidt process, special matrix properties, and factorizations and decompositions like QR and SVD, equipping students with advanced tools for complex problem-solving in data science and AI.
Your instructor
Instructor · LUNARTECH
Tatev Aslanyan
Tatev brings industry experience, advanced AI/ML degrees and a reputation as a thought leader in data science to LUNARTECH. She holds Bachelor’s and Master’s degrees in STEM, and her publications in top journals and presentations at international conferences showcase her expertise.
How you get there
Top-tier roles go to people who can do the work.
Top-tier roles go to people who can do the work.
Here’s how you get there.
Work it through, step by step.
Gaussian elimination, inverses and determinants, worked until the method is yours.
See what it means.
The geometry comes with the algebra, so you can picture what a matrix does before you compute it.
Take it into real work.
Carry it into data science, machine learning and AI, down to the QR and SVD behind the models.
Support
Support at every stage.
Support at every stage.
You won’t be working through this alone.
Before you start
Try it first.
A 3-day free trial opens a selection of the content. Your card is only charged once it ends.
While you learn
Mentors within reach.
Stuck on a concept? Reach out to a mentor whenever you need help.
While you learn
One-on-one sessions.
On the yearly plan, one-on-one sessions give you dedicated support.
Any time
A team behind you.
Write to info@lunartech.ai at any point, from your trial onwards. If your employer is funding you, we’ll set it up with them directly.
All the way through
A schedule that fits around your life.
80 hours in totalYour own paceFrom anywhereAt any hour
After the last lesson
Stay in the network.
Your alumni network stays with you: ongoing support, opportunities and industry insight.
Career support
Career support, past the last lesson. Coaching, a sharper resume, real interview preparation and the people to know.
Career direction
Tailored coaching helps you decide where to aim and how to get there.
Strong portfolio
Hands-on projects become work you can show, not just claim.
Resume and profile
Personalized refinement, so what you send says what you can actually do.
Interview preparation
Preparation for the questions that decide it, so you walk in ready.
Network and search
Connections with industry leaders, and an alumni network that stays with you.
Reviews
Real stories from the community.
LUNARTECH Academy has been the most empowering learning experience of my life, giving me a clear, structured path from the absolute basics to building real-world AI systems with confidence.
I’m really enjoying your linear algebra video. It’s been very valuable.
I’m going through your mathematics course. It’s amazing. Thank you for putting it together.
Thank you for the helpful videos. They’ve taught me a lot. I’m excited to continue with your linear algebra course.
Your page is fantastic. As a bachelor’s student in Data Science now accepted for a master’s at UConn, your work has been a real source of motivation.
The programme’s clear, bite-sized content and practical projects dramatically improved my speed from fuzzy idea to MVP and my ability to communicate AI value. I followed the system, and it works.
I really appreciate your teaching style and the way you break down complex topics. It has been incredibly helpful.
After years working mainly with R for econometrics, I found your Python machine learning course a refreshing and engaging way to learn Python.
As a Data Science graduate, I want to thank you for the effort you put into making videos to support growing data scientists.
I’ve been following your work since taking your machine learning course, and I’m impressed by your practical approach to applying AI.
Why choose us
Built around how you actually learn.
One standard behind every course, from the first lesson to long after the last.
Hands-on practice
Apply every idea to real problems, so it becomes something you have used, not only seen.
Industry-aligned curriculum
We keep courses current with the tools, techniques and skills the field asks for.
Flexible learning
Study at your own pace, from anywhere, at any hour.
Certificate of completion
Finish the course and earn a certificate that shows what you have learned.
Focus on your success
Personalized learning plans and support structures carry you through the hard parts.
Lifetime alumni network
Stay connected after you finish, with ongoing support, opportunities and industry insight.
Your certificate
It doesn’t raise its voice. Neither will you.
Finish the course and it is issued in your name, under our signature. There is no other way to get one.
Certificate of completion
Your Name
Fundamentals to Linear Algebra
LUNARTECH RISE Academy
Pricing
This course comes with the membership.
This course comes with the membership.
So does everything else.
One membership opens every course, certification, workshop and masterclass in the Academy. Every plan starts with a 3-day free trial.
3 days free, then $29.97 a month. Your card is only charged once the trial ends.
Included in every plan
- Every course in the Academy
- Every certification course
- Workshops and masterclasses
- A certificate of completion
- A 3-day free trial
- Learning at your own pace
- The lifetime alumni network
- Upgrades at any time
In practice
Six modules. Eight professions.
Six modules. Eight professions.
One mathematics underneath them all.
Every role uses all six modules. Here’s where each one leans hardest, and where its work ends up.
- 01Foundations
- 02Vectors
- 03Matrices
- 04Systems
- 05Transforms
- 06Factorization
-
Each neural network layer multiplies by a matrix. SVD shrinks the data before it gets there.
Vectors, Matrices, Factorization
Language models and agents, Search and recommendation, Finance and trading
-
Retrieval ranks documents by the dot product of their embeddings. Attention runs on the same operation.
Foundations, Vectors, Matrices
Language models and agents, Search and recommendation
-
Risk lives in a covariance matrix. Decomposing it shows what really drives a portfolio.
Matrices, Systems, Factorization
Finance and trading, Forecasting and pricing
-
A regression projects data onto a column space. Rank shows when two features say the same thing.
Vectors, Systems, Factorization
Search and recommendation, Forecasting and pricing, Healthcare and medical imaging
-
An image is a matrix and a camera is a transformation. SVD recovers 3D geometry from matched points.
Matrices, Transforms, Factorization
Healthcare and medical imaging, Robotics and manufacturing, Autonomous vehicles and drones
-
An arm’s pose is a chain of matrix multiplications. Solving linear systems tells each joint how to move.
Matrices, Systems, Transforms
Healthcare and medical imaging, Robotics and manufacturing, Autonomous vehicles and drones
-
A rotation matrix holds an aircraft’s attitude. A GPS position comes from solving linear equations.
Foundations, Systems, Transforms
Autonomous vehicles and drones, Aerospace and satellites
-
Matrices carry every 3D object onto the screen. The dot product decides how light falls on it.
Vectors, Matrices, Transforms
Games, film and simulation
- Language models and agents
- Search and recommendation
- Finance and trading
- Forecasting and pricing
- Healthcare and medical imaging
- Robotics and manufacturing
- Autonomous vehicles and drones
- Aerospace and satellites
- Games, film and simulation
Machine Learning Engineer
Each neural network layer multiplies by a matrix. SVD shrinks the data before it gets there.
Over 10,000 students trust LUNARTECH
LUNARTECH gives you the skills
to learn, build, create and lead.
Engineers
Understand systems all the way down. Build the ones others rely on.
Scientists
Understand what the data says. Build models that hold up.
Researchers
Understand the papers. Build on them, and take the work further.
The field
Anyone can use AI.
Anyone can use AI.
Few can engineer it. This is where that starts.
+340%growth in open roles requiring AI skills
Roles and pay
~35,000 open roles right now
Open roles: Built In, Greenhouse, LinkedIn.
Typical salaries: Glassdoor, Levels.fyi, Payscale, Indeed, Ravio, JobRise, U.S. BLS. Military: 2026 U.S. basic pay, drone officers with aviation incentive pay.
Updated November 2026.
FAQ
Frequently asked questions.
Need help? These answers cover most of what people ask before they start.
Our 3-day free trial gives you access to a selection of content in the bootcamps, courses and materials, so you can experience the value of our content first-hand. This includes comprehensive learning materials and interactive sessions. You won’t be charged during this period, though we require your credit card details at the start to ensure a seamless transition should you choose to continue.
Yes, entering your credit card details is a necessary step to begin your free trial. The process is entirely secure, and we ask for it to provide a seamless transition to a paid subscription if you decide to continue beyond the trial. You will only be charged after the trial period ends, with full access to our content based on the plan you choose.
After your 3-day free trial you gain access to the full breadth of our content, depending on the subscription plan you choose. We offer free trials for our monthly, bi-annual and annual plans, and each plan provides a different scope of access and benefits.
If your employer has agreed to fund your learning, in part or in full, please contact us at info@lunartech.ai. We’ll work with you and your employer to set up everything needed for your subscription.
Yes. Our support remains strong both during your free trial and after you subscribe. Reach the team at info@lunartech.ai with any question, whether you’re onboarding, navigating your trial, or need help as a member. Subscribers to the yearly plan also receive dedicated support in one-on-one sessions.
You can upgrade your plan at any time during your subscription. Downgrading is not available for bi-annual or annual plans, but you can cancel and then choose a new plan that suits you better. For bi-annual and annual plans we also offer payment in instalments; please reach out to learn more.
The foundation
Start with the mathematics every model depends on.
Eighty hours that take linear algebra from the first vector to the factorizations behind modern AI. Begin with a free lesson, or enroll in the full course.
