Prerequisites in place
Use norms, Euclidean distance and trigonometry on the Cartesian plane and the unit circle to solve vector problems.
Partners and press
Overview
A vector has a length and a direction. The dot product compares two of them.
A three-hour course on vectors from the ground up. It begins with the prerequisites: norms and Euclidean distance, real numbers and vector spaces, the Cartesian coordinate system and the unit circle.
Then it covers vector definitions and operations, special vectors such as the zero vector and unit vectors, scalar multiplication and linear combinations, and ends on the dot product, projections, angles and the Cauchy-Schwarz Inequality.
3Hours
3Modules
4.9Academy rating
10,000+Students
What you’ll learn
Learn all the way down.
Learn all the way down.
Perform when it matters.
The language of vectors
Define vectors, carry out their basic operations, and recognize the zero vector and unit vectors and what makes them special.
Linear combinations
Scale vectors and combine them into linear combinations, using them to manipulate and analyze vectors.
The dot product, interpreted
Calculate dot products, read them as projections and angles, and see what the Cauchy-Schwarz Inequality says about them.
Course outline
Three modules, from a norm
Three modules, from a norm
to the Cauchy-Schwarz Inequality.
See why prerequisites matter, then refresh norms and Euclidean distance, real numbers and vector spaces, and the Cartesian coordinate system and unit circle.
Learn what a vector is and its basic operations, meet special vectors such as the zero vector and unit vectors, and use scalar multiplication and linear combinations.
Discover the dot product and its geometric significance: how it relates to projections and angles, and what the Cauchy-Schwarz Inequality tells you.
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.
Set the groundwork.
Refresh norms, Euclidean distance, the Cartesian system and the unit circle before you use them.
Learn what vectors can do.
Define vectors, apply their operations, and combine them with scalar multiplication.
Compare two vectors.
Use the dot product to relate vectors through projections and angles, and bound it with Cauchy-Schwarz.
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.
3 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
Vector Fundamentals
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
Three modules. Four professions.
Three modules. Four professions.
One object under a great deal of applied math.
Every role uses all three modules. Here’s where each one leans hardest, and where its work ends up.
- 01Foundations
- 02Operations
- 03Dot product
-
Represents records as vectors and compares them. Uses norms and distances to measure how alike they are.
Operations, Dot product
Data science
-
Reads model inputs as vectors in a space. Uses the dot product the way a model does.
Foundations, Operations, Dot product
Machine learning
-
Computes angles and projections for every object. Works on the Cartesian plane and the unit circle.
Foundations, Dot product
Computer graphics
-
Resolves a force into components with projections. Combines vectors to find a resultant.
Foundations, Operations, Dot product
Engineering
- Data science
- Machine learning
- Engineering
- Computer graphics
Data Scientist
Represents records as vectors and compares them. Uses norms and distances to measure how alike they are.
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.
The prerequisites: norms and Euclidean distance, real numbers and vector spaces, the Cartesian coordinate system and the unit circle.
No. It stays on vectors: their definition, operations, linear combinations and the dot product.
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 short foundation
Learn the vector before you build on it.
Three hours from norms and distance through vector operations to the dot product and its geometry. Begin with a free lesson, or enroll in the full course.
