Hello Bioinformatics lovers,

Tommy again! Can you believe we are at the end of 2025?

Focus on the most important things to do so you can achieve what you wanted to do at the beginning of 2025.

Today, we will talk about linear algebra.

I have a confession: I nearly failed linear algebra in college.

I scraped by with a D, thought "when will I ever need this?", and promptly forgot everything.

Calculus wasn't much better.

Fast forward to today.

I'm staring at a Seurat PCA projection that won't behave, and I realize: I'm paying for that D every single week.

Here's what I wish someone had told me then:

Every matrix you work with in bioinformatics—and you work with them constantly—is linear algebra in action.

Your RNA-seq data? That's a gene-by-sample matrix.

Your single-cell counts? Gene-by-cell matrix.

ChIP-seq peaks? Peak-by-sample matrix.

Drug response screens? Drug-by-sample matrix.

And every time you run PCA, cluster cells, or reduce dimensions, you're applying linear algebra operations to those matrices.

Understanding what's actually happening under the hood transforms you from someone who runs commands to someone who knows why those commands work—and what to do when they don't.

The breaking point:

Last month, I decided to truly understand how Seurat's PCA projection and label transfer work at a mathematical level.

I spent 6 hours over 3 nights working through the matrix operations. It was hard. My brain hurt. But something clicked.

Now when my PCA acts weird, I don't just try random parameters. I understand what's happening to my data matrix at each step. I can debug intelligently. I can explain results to collaborators with confidence.

You can do this too:

If you feel shaky on linear algebra (join the club—most of us do), MIT OpenCourseWare has the gold standard free course: MIT 18.06 Linear Algebra by Gilbert Strang.

Direct link: https://web.mit.edu/18.06/www/​

You will love this 2blue1brown video too on eigenvalues https://www.3blue1brown.com/lessons/eigenvalues​

Yes, it's a time investment. But unlike most online courses you bookmark and never finish, this one pays immediate dividends in your daily work.

I also wrote up my deep dive into Seurat's PCA mechanics for single-cell RNA-seq.

Fair warning: it's technical. But if you want to see how matrix factorization applies to real single-cell analysis, check it out:

• Matrix factorization in single-cell: https://divingintogeneticsandgenomics.com/post/matrix-factorization-for-single-cell-rnaseq-data/​
• Seurat PCA projection explained: https://divingintogeneticsandgenomics.com/post/pca-projection/​

Bottom line:

It's never too late to learn what you should have learned earlier.

Your past self made decisions with the information they had. Your current self can make different choices.

I'm still catching up on math I should have mastered 15 years ago.

But I'm better at my job every week because of it.

Your turn: What's the one skill you wish you'd learned properly the first time?

Hit reply—I'd genuinely love to know what other learning gaps people are filling.

And if you're already solid on linear algebra, what's the math or CS concept you think more bioinformaticians should understand?

Happy Learning!

Tommy aka crazyhottommy

PS:

If you want to learn Bioinformatics, there are other ways that I can help:

1. My free YouTube Chatomics channel, make sure you subscribe to it.
2. I have many resources collected on my github here.
3. I have been writing blog posts for over 10 years https://divingintogeneticsandgenomics.com/​

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Stay awesome!