Transformations, explained
Say what makes a transformation linear and describe how it changes the space around it while preserving its key properties.
Partners and press
Overview
A transformation changes space. A matrix is how you write it down.
A two-hour course on linear transformations, the operations that change the space around us while preserving essential properties. You start with their geometry: rotation, scaling and reflection.
Then you learn the matrices that represent them and the laws those matrices follow, with determinants, inverses and the transpose, and end on where the transpose is used in transformation problems.
2Hours
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.
Shapes that move
Picture how transformations rotate, scale and reflect shapes, so the geometry is clear before the algebra starts.
Matrix laws and tools
Apply the basic operations and algebraic laws of matrices, then use determinants and inverses to read and undo a transformation.
The transpose, in use
Know the properties of the transpose and see where it comes up when you work with linear transformations.
Course outline
Six short modules, from one idea
Six short modules, from one idea
to the transpose in use.
Start with the core idea of a linear transformation: an operation that changes the space around us while preserving essential properties.
Visualize how linear transformations act on shapes and space, including rotations, scaling and reflections.
Learn the basic operations and the algebraic laws that govern matrices, the main tools for representing linear transformations.
Use determinants to reveal key properties of a matrix, and matrix inverses to undo a transformation.
Understand what the transpose does, the properties it has, and its role in manipulating matrices for linear transformations.
See the transpose at work in real transformation scenarios, which can include image manipulation and data analysis.
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.
See what it does to space.
Begin with the picture: how a linear transformation takes a shape and turns, scales or flips it.
Write it as a matrix.
Use matrix operations and laws to represent a transformation, then read it through its determinant and inverse.
Finish with the transpose.
Study the properties of the transpose, then see how it applies inside linear transformations.
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.
2 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
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Interview preparation
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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.
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Why choose us
Built around how you actually learn.
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Hands-on practice
Apply every idea to real problems, so it becomes something you have used, not only seen.
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Finish the course and earn a certificate that shows what you have learned.
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Lifetime alumni network
Stay connected after you finish, with ongoing support, opportunities and industry insight.
Your certificate
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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 Transformations
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
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In practice
Six modules. Four professions.
Six modules. Four professions.
One idea behind how images and data are reshaped.
Every role uses all six modules. Here’s where each one leans hardest, and where its work ends up.
- 01Transformations
- 02Geometry
- 03Matrices
- 04Det and inverse
- 05Transpose
- 06Transpose in use
-
Rotates, scales and reflects images with matrices. Reverses an edit with an inverse.
Transformations, Geometry, Transpose in use
Image manipulation
-
Transforms datasets with matrix operations. Checks the result with a determinant or a transpose.
Matrices, Transpose in use
Data analysis
-
Reads a model’s weights as transformations. Manipulates matrices with the transpose.
Matrices, Det and inverse, Transpose
Machine learning
-
Describes how a body turns, stretches or flips. Reverses the motion to get back to the start.
Transformations, Geometry, Det and inverse
Engineering
- Image manipulation
- Data analysis
- Engineering
- Machine learning
Image Processing Engineer
Rotates, scales and reflects images with matrices. Reverses an edit with an inverse.
Over 10,000 students trust LUNARTECH
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The field
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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.
No. It stays with linear transformations, matrices, determinants, inverses and the transpose.
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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.
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A short foundation
Understand a transformation, then its matrix.
Two hours that take linear transformations from their geometry to determinants, inverses and the transpose. Begin with a free lesson, or enroll in the full course.
