If you’ve made it to linear algebra and suddenly feel lost, you’re not alone. You might’ve done just fine in algebra and calculus — maybe even excelled. But now, with matrices, vector spaces, and all these new definitions, it feels like the rules have changed. And in a way, they have. Linear algebra is a different kind of math. It’s more abstract, more symbolic, and more about structure than steps. That shift can feel like hitting a wall — especially if no one warned you it was coming. But the wall isn’t a dead end. It’s just a signal that you need new tools and a different mindset.

1. You're Working with More Abstraction

In earlier math classes, you spent a lot of time calculating — solving for x, taking derivatives, integrating functions. The problems were familiar and concrete.

Linear algebra introduces abstract objects like vector spaces, spans, and null spaces. Instead of just finding a number, you’re asked to reason about collections of vectors, about transformations between spaces, and about whether something is always true.

That’s not a bad thing — but it is a shift. And it takes time to adjust.

What you can do:

• Focus on what a concept means, not just how to compute it.

• Ask yourself: “Can I explain what this is in my own words?”

• Don’t rush to solve — slow down and understand the structure first.

📺 Need a refresher? Watch my introduction to vector spaces on YouTube

2. The Notation Feels Overwhelming

IIn linear algebra, the notation can be dense. Vectors, matrices, transposes, subscripts, norms — it’s a lot to take in. And if the notation isn’t clear, even simple ideas feel harder than they are.

Sometimes the problem isn’t your understanding — it’s that the symbols haven’t become familiar yet.

What you can do:

• Create your own “notation cheat sheet” with clear labels.

• Don’t be afraid to write out longhand versions of equations if the symbols are getting in the way.

• When studying, explain the notation out loud to yourself — this helps more than you’d think.

📝 Check out my free guided notes for help with notation and definitions.

3. You're Not Sure Why You're Learning This

Let’s be honest — some concepts in linear algebra feel disconnected at first. What does it mean to “span a space”? Why does “linear independence” matter? And what is the point of a “basis”?

When you can’t see the purpose, it’s hard to stay motivated.

But here’s the thing: linear algebra shows up everywhere — in engineering, computer science, graphics, statistics, and even machine learning. Once you understand it, you’ll start seeing it behind problems you didn’t even realize were mathematical.

What you can do:

• Look for simple real-world applications — systems of equations, projections, data compression.

• Ask your instructor for an example of how this concept is used in practice.

• Know that the deep understanding comes later — for now, keep building the foundation.

🎥 Curious about span and linear independence? Here’s a video that walks through them with examples.

4. It Builds on Itself — Quickly

Linear algebra is cumulative. If you don’t fully understand span, then linear independence won’t make sense. If you don’t get linear independence, the idea of a basis will feel confusing. And without a solid grasp of a basis, good luck understanding change of coordinates.

If you miss something early, it creates a chain reaction.

What you can do:

• Review early concepts regularly. Even 10 minutes a day helps.

• Go back to basics when you feel stuck. Often the issue is upstream.

• Don’t wait — the earlier you clear up confusion, the easier everything becomes.

🧠 Try working through the video playlist step-by-step alongside the notes — repetition builds understanding.

5. You're Not Struggling — You're Learning Differently

This subject may feel harder, but it’s not because you’re not capable. You’re just being asked to think at a different level — to connect ideas, use definitions carefully, and work with abstract systems.

It’s a different kind of thinking, and that takes time.

What you can do:

• Treat confusion as part of the process, not a failure.

• Keep going, even if your progress feels slow.

• Celebrate the moments when something clicks — because those will come.

Final Thoughts

Linear algebra asks more from you — not just more effort, but more reasoning, more reflection, and more patience. If you feel like you’re hitting a wall, it doesn’t mean you’re not good at math. It means you’re at the point where real mathematical thinking begins.

Take it one definition at a time. Work through examples. Revisit concepts. Draw diagrams. Ask questions. And keep going — you’ll get through the wall, and when you do, you’ll realize it wasn’t a wall at all. Just a doorway into a new way of seeing mathematics.