Transformations you can picture
Explain what a linear transformation preserves and show how it rotates, scales, reflects or distorts shapes and space.
Partners and press
Overview
Transformations move space. Factorizations show how they’re built.
A five-hour course that starts from the geometry of linear transformations, how they rotate, scale, reflect and distort shapes, and works toward the matrices that represent them.
Along the way you cover determinants, inverses, the transpose, vector spaces, bases and projections. It ends on matrix factorization: special matrices, then QR, eigen and singular value decomposition.
5Hours
6Modules
4.9Academy rating
10,000+Students
What you’ll learn
Learn all the way down.
Learn all the way down.
Perform when it matters.
Matrix operations with a purpose
Add, subtract and scale matrices, and use determinants, inverses and the transpose to describe and undo transformations.
Vector spaces and projections
Work with a vector space and its basis, and use vector projections to solve geometric problems.
Matrices broken into parts
Recognize special matrices and follow the ideas behind QR, eigen and singular value decompositions.
Course outline
Six modules, from a transformation
Six modules, from a transformation
to singular value decomposition.
Start with linear transformations, the mathematical operations that change space while preserving specific properties.
Learn to visualize a transformation and see how it rotates, scales, reflects and distorts shapes.
Work through matrix addition, subtraction and scalar multiplication, the basic tools for representing linear transformations.
Use determinants to learn key facts about a matrix, inverses to undo a transformation, and the transpose to manipulate matrices.
Understand what a vector space is and what its basis is, and use vector projections as a geometric tool.
Meet special matrices with unique properties, then break matrices into simpler components with QR, eigen and singular value decomposition.
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.
Picture the transformation.
Start with what a linear transformation does to shapes before you work with any matrix.
Write it as a matrix.
Represent the transformation with a matrix, then use its determinant and inverse to read and reverse it.
Break the matrix down.
Finish by factorizing a matrix into simpler components with QR, eigen and singular value decomposition.
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.
5 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
Linear Algebra Tools
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. Four professions.
Six modules. Four professions.
One toolkit for reshaping and compressing data.
Every role uses all six modules. Here’s where each one leans hardest, and where its work ends up.
- 01Transformations
- 02Geometry
- 03Matrices
- 04Det, inverse, T
- 05Vector spaces
- 06Factorization
-
Applies transformations to images and shapes. Undoes a transformation to get back to the original.
Transformations, Geometry, Det, inverse, T
Image processing
-
Reduces a large matrix to its strongest parts. Knows when a factorization is the right tool.
Vector spaces, Factorization
Data compression, Data science
-
Reads a model’s matrices as transformations of space. Uses decompositions to simplify or compress them.
Matrices, Det, inverse, T, Factorization
Recommendation systems, Data science
-
Rotates, scales and reflects objects with matrices. Checks what a transformation does to shape and area.
Transformations, Geometry, Matrices
Image processing
- Image processing
- Data compression
- Recommendation systems
- Data science
Computer Vision Engineer
Applies transformations to images and shapes. Undoes a transformation to get back to the original.
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.
Special matrices and matrix factorization: breaking a matrix into simpler components with QR, eigen and singular value decomposition.
Yes. One module covers vector spaces, their basis and vector projections.
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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 toolkit
Take a matrix apart and see how it works.
Five hours from linear transformations to QR, eigen and singular value decompositions. Begin with a free lesson, or enroll in the full course.
