Was just coming in to point to this. While the geometric intuition in the post being discussed is quite visual, thinking of matrix elements as directed arrows g

Was just coming in to point to this. While the geometric intuition in the post being discussed is quite visual, thinking of matrix elements as directed arrows generalizes easily to high-dimensional vector spaces, and also makes it very easy to understand the behavior of sparse transformation matrices, and motivates a nice correspondence between linear algebra and graph algorithms (ref. graphblas)