Vectors, Dimensions, and Feature Spaces — The Geometry Behind Machine Learning

If you strip machine learning of all the complex terminology and buzzwords, you almost always end up with the same core idea: we represent real-world objects as numbers and work with those numbers mathematically. This is where vectors, dimensions, and feature spaces come in. As PHP developers, it’s especially important to understand this intuitively rather than formally, because in code you’ll deal not with abstract linear algebra, but with arrays of numbers, matrices, and operations on them. A