concept linear map in category python

This is an excerpt from Manning's book Math for Programmers: 3D graphics, machine learning, and simulations with Python MEAP V11. Login to get full access to this book.

In general, an m-by-n matrix defines a function taking n-dimensional vectors as inputs and returning m-dimensional vectors as outputs. Any such function is linear in the sense that it preserves vector sums and scalar multiples. It’s not a transformation because it doesn’t just modify input, it returns an entirely different kind of output: a vector living in a different number of dimensions. For this reason, we’ll use a more general terminology; we’ll call it a linear function or a linear map. Let’s consider an in-depth example of a familiar linear map from 3D to 2D.

Figure 6.26: A linear map takes any image (left) and returns a new one (right) that lies in a 900-dimensional subspace.