In the previous post, I described a simple way to think about matrices, namely as bipartite graphs. Today I'd like to share a different way to picture matrices—one which is used not only in mathematics, but also in physics and machine learning. Here's the basic idea. An $m\times n$ matrix $M$ with real entries represents a linear map from $\mathbb{R}^n\to\mathbb{R}^m$. Such a mapping can be pictured as a node with two edges. One edge represents the input space, the other edge represents the...
