Vectors you can work with
Represent vectors, add, subtract and scale them, and picture how they describe data in practical scenarios.
Partners and press
Overview
Vectors, matrices and linear systems. The groundwork, in seven hours.
A seven-hour introduction to linear algebra for AI and data science. It opens with a refresher on the math you need, then covers vectors, matrices and the dot product.
From there you solve linear systems with Gaussian elimination and Reduced Row Echelon Form, and finish with a preview of symmetric and diagonal matrices, how linear algebra is coded and where it’s applied.
7Hours
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.
Matrices that structure data
Tell the main types of matrix apart, add, subtract and multiply them, and see how matrices carry out transformations of data.
The dot product, geometrically
Read the dot product as a geometric idea tied to vector length, and use it with the cosine rule to solve problems.
Systems solved step by step
Solve linear systems with Gaussian elimination, and use Reduced Row Echelon Form to reach the solutions cleanly.
Course outline
Six modules, from a refresher
Six modules, from a refresher
to a preview of what’s ahead.
Refresh the essential math prerequisites and get a high-level view of how linear algebra is applied across AI, data science and emerging technologies.
Build a working understanding of vectors: how they are represented, how to add, subtract and scale them, and how they appear in practical data scenarios.
Learn the different types of matrix, how they structure data and how to add, subtract and multiply them, then see how matrices power data transformations.
Understand the dot product, its geometric meaning and its link to vector length, then apply the cosine rule and related ideas to solve problems.
Learn the idea of solving a system of linear equations with Gaussian elimination, and how Reduced Row Echelon Form streamlines finding the solutions.
Get a first look at specialized matrices such as symmetric and diagonal ones, how linear algebra is written in code, and its broad applications.
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.
Refresh the groundwork.
Review the math prerequisites, then meet vectors, matrices and the operations that combine them.
Measure with the dot product.
Use the dot product for length and angle, and apply the cosine rule to solve problems.
Solve the system.
Reduce a linear system with Gaussian elimination, then read the solutions off its reduced row echelon form.
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.
7 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 Essentials
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 foundation under the math of modern data work.
Every role uses all six modules. Here’s where each one leans hardest, and where its work ends up.
- 01Crash course
- 02Vectors
- 03Matrices
- 04Dot product
- 05Linear systems
- 06Preview
-
Treats a dataset as vectors and matrices. Reads similarity between records off a dot product.
Vectors, Matrices, Dot product
Data science teams
-
Follows what the matrices inside a model are doing. Solves the small systems that sit underneath it.
Matrices, Linear systems, Preview
AI and machine learning
-
Organizes records into matrices before analysis. Uses vector operations to compare and combine them.
Vectors, Matrices
Data science teams
-
Reads the linear algebra inside a published method. Writes the idea as code once the notation is clear.
Crash course, Dot product, Preview
AI and machine learning, Research
- AI and machine learning
- Data science teams
- Engineering
- Research
Data Scientist
Treats a dataset as vectors and matrices. Reads similarity between records off a dot product.
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.
As a preview. The last module shows how linear algebra is coded and where it’s applied, alongside specialized matrices such as symmetric and diagonal ones.
With a quick refresher on the essential math prerequisites and an overview of how linear algebra is applied across AI and data science.
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.
A first pass
Learn the core of linear algebra.
Seven hours from a refresher through vectors, matrices and linear systems to a preview of what comes next. Begin with a free lesson, or enroll in the full course.
