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Why I’m Finally Studying Linear Algebra Again (And How It’s Helping Me Build an AI Agent)
- Juan Pablo Camacho
- Feb 13
- 2 min read
Updated: Feb 13
Do We Really Need to Study This?
I still remember sitting in my university linear algebra class, looking at a blackboard full of matrices and vectors, thinking, When am I ever going to use this? Fast forward to today, and here I am—back at it, relearning the same concepts I once dismissed. Except this time, I actually want to understand them because they’re the foundation of something I never saw coming: AI agents.
The Unexpected Return to Vectors
I'm not the best at explaining the concept, but if you're like me and never really understood vectors, check out this video: Understanding Vectors. As I dive into the world of AI agents, I’ve realized that one of the first fundamental concepts I need to grasp is vectors. Yes, those same vectors that I once ignored, thinking they were just abstract arrows in space. Now, they’re at the heart of how AI understands and processes information.
For example, when building an AI-powered agent for personalized ad creation, everything starts with vectors. Why? Because in AI, data isn’t just raw numbers—it’s transformed into vector representations. Text, images, user behaviors, and even ad preferences are mapped into multi-dimensional vector spaces, allowing AI to detect patterns, similarities, and trends that would otherwise be impossible to recognize.
What Are Vectors, and Why Do They Matter?
If you’re like me, and the word "vector" only brings back memories of confusing math problems, let’s break it down simply:
A vector is essentially a list of numbers that define a point in space. But instead of just existing in a simple 2D or 3D space, in AI, vectors exist in much higher dimensions. This allows us to represent complex relationships.
Let’s say we want an AI agent to generate a personalized ad for a specific user. That user’s preferences, previous interactions, and behaviors can be turned into a vector representation—a unique fingerprint that helps the AI understand who they are and what kind of ad would resonate with them the most.
My "Aha!" Moment
The moment it all clicked for me was when I saw how word embeddings work in AI. Words can be represented as vectors, where words with similar meanings are closer together in space. This means AI can understand context, sentiment, and intent in ways I never imagined.
Now, imagine applying this concept to ads. Instead of generic, one-size-fits-all campaigns, my AI agent could analyze user behavior, map out key interests, and dynamically create customized, hyper-relevant ads—all thanks to the power of vectors.
Conclusion: Maybe That Professor Was Right
I used to think that learning about vectors and linear algebra was just an academic exercise with no real-world application. Now, I see that it’s the key to unlocking AI-powered personalization.
So, if you’re like me and ever questioned Why do I need to study this?—surprise! It might just end up being the foundation of something incredible you’ll build in the future.
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