anyone else struggling with linear algebra this semester?

Linear algebra is one of those courses where the gap between following a lecture and solving problems independently is massive. What helped me most was working through the proofs by hand, not just the computational exercises. When you prove why eigenvalues behave a certain way, the problem-solving strategies start making sense because you understand the underlying logic rather than just memorizing steps.

For eigenvalues specifically: make sure your determinant calculations are solid. Most of the errors I made early on traced back to arithmetic mistakes in computing det(A - lambda*I), not conceptual misunderstanding. Practice the mechanical part until it's automatic and then focus on interpretation. What does it mean geometrically when a matrix has repeated eigenvalues? What happens when eigenvalues are complex? Those conceptual questions are what separate students who can do the calculations from students who actually understand the material.

3Blue1Brown's linear algebra series on YouTube is genuinely excellent for building geometric intuition. It won't replace your textbook but it gives you a visual framework that makes the abstract concepts click. I'd watch the relevant video before each lecture, not after. Going in with a visual mental model makes the formal notation much easier to absorb.

Same boat here. What's working for me so far is rewriting the key definitions and theorems in my own words after each lecture, almost like translating them into plain English. For eigenvalues, I wrote something like: "An eigenvalue is a scalar that tells you how much a transformation stretches or compresses along a particular direction." That one sentence clarified more than an hour of notation-heavy lecture.

@chris_patel is right about the 3Blue1Brown series. The visual intuition is a game changer, especially for understanding transformations, span, and null spaces. Also, if your textbook is Strang, the MIT OpenCourseWare lectures that go with it are free and very good. Strang explains things in a way that complements the textbook because he focuses on intuition during lectures and saves the rigor for the written material. I watch the lecture first and then read the corresponding chapter, and the combination works better than either alone.

I took linear algebra last year and eigenvalues were the exact point where I hit a wall too, so you're not alone. This seems to be a universal experience. Two things that made the difference for me:

First, I started going to office hours every single week. Not because I had specific questions every time, but because hearing the professor explain concepts in a less formal setting clicked differently than lecture. Other students would ask questions I hadn't thought of, and those discussions filled gaps I didn't know I had. The professor also tends to share which types of problems appear on exams, which helps you prioritize what to study.

Second, I formed a study group with two other people from my section. We'd each attempt the problem set independently and then meet to compare approaches. Seeing how someone else set up the same problem exposed me to different strategies and caught my blind spots early. Linear algebra rewards multiple perspectives because there are often several valid approaches to the same problem. One person might solve it using row reduction while another uses the determinant directly, and understanding both methods deepens your grasp of the underlying structure.

Study groups are honestly the way to go for this course. Linear algebra is one of those subjects where explaining a concept to someone else forces you to understand it at a deeper level. Also, if your university has a math help center or tutoring drop-in, use it early in the semester before the midterm rush. The tutors are way less overwhelmed in weeks three through five than they are in week eight.