Most developers jump into machine learning through Python libraries like Scikit-Learn, TensorFlow, or PyTorch. But if you’ve ever wondered how these libraries actually work under the hood, the answer is almost always linear algebra.
So, what is it? At a basic level, linear algebra deals with vectors, matrices, and transformations. In ML, data is stored in these formats, and algorithms perform operations on them to find patterns and make predictions.
Here’s where you’ll see linear algebra in action:
Linear Regression: predictions are solved using matrix operations.
PCA (Principal Component Analysis): uses eigenvalues and eigenvectors for dimensionality reduction.
Neural Networks: every forward pass and backprop step is matrix multiplication.
Support Vector Machines: use dot products to calculate hyperplanes.
In practice, this math powers everyday AI applications: image recognition, NLP models, recommendation systems, and speech-to-text engines.
If you’re a developer, the good news is you don’t need to master every theorem. Focus on what matters for ML:
Vectors and matrices
Matrix multiplication
Dot product
Eigenvalues and eigenvectors
This foundation makes debugging, fine-tuning, and even building custom ML models much easier.
At the end of the day, linear algebra is not just theory—it’s the language of data. And if you want to move from “using libraries” to actually understanding machine learning, this is where your journey should start.
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