Two Forms of the Dot Product

Knowing which quadrant you’re working in will help you make good decisions about the forms you’ll use, the time you’ll need, and the skills you’ll call on. Let’s start at the top left of this 2×2 and proceed counterclockwise.

“V” stands for visualization.

When you study vector spaces, you also study the concepts of linear maps, kernel, rank, dimension, and codimension. Vector spaces are usually represented by letters and linear maps by arrows connecting these letters. But when I chose to picture vector spaces as bigger or smaller barrels (according to their dimension) and linear maps as bigger or sm

you can think of the metric tensor as being a black box; you put two vectors in, and a number comes out.