Is vector geometry useful within economics?

I'm going to be taking a semester of math after my bachelor's in economics before I go on to do a master's, and one of the mandatory courses in that semester is linear algebra with a focus on vector geometry. This is how they describe it:

The course gives an introduction to elementary linear algebra with a focus on vector geometry.

Analytic geometry in two and three dimensions: vectors, bases and coordinates, linear dependence, equations of lines and planes, inner product, quadratic curves, calculation of distances and angles, vector and volume product, calculation of area and volume.

Is this stuff useful within economics? I'm fairly sure the other courses are useful but I'm unsure about this one, partly I guess because I don't have a clear picture of what vector geometry really is. The course is not designed specifically for economics students so that's why I'm asking.

Solution 1:

Econometrics is largely mathematics. If you want to be able to understand it, you have to know the math behind it. Otherwise you will be in a perpetual struggle to grasp the math in what you are learning. So, yes, it is relevant.

Solution 2:

A really vivid example is Modern Portfolio Theory (MPT) (Nobel Prize in economics). Linear algebra (or vector geometry) deals with matrices a lot, and these 3 articles show how to deal with MPT (specifically, how to calculate the efficient frontier) using just vectors and matrices

• part 1
• part 2
• part 3

If later you decide to become a quant, this is an example of topics you'd expect to be familiar with (and MPT is there).

Solution 3:

As others have pointed out, Linear Algebra is very relevant in economics. I would say that it universally the most useful "higher-level" mathematics (i.e. excluding basic algebra), both in terms of applications and in studying other higher-level math.

But, as you point out, it is not obvious why the focus is on vector geometry. To understand this, you need to know a bit about Linear Algebra. At least at the elementary level, it is a very much a mix of algebra and geometry. However, it can be taught, and often is taught, only from the perspective of algebra. In my experience, this just results in most students being confused by the material, both in terms of understanding the content and its actual purpose/motivation. By teaching the geometry, and getting students to think in terms of the geometry, they actually understand the algebra better.

Now, in this particular case, it is not clear if this is exactly the intent of the class. It seems even somewhat more focused on geometry than I personally think makes sense, so the intent might be different (no way to know without context, of course). Nevertheless, you'll likely find it gives a solid foundation in a very important field of math.

Lastly, I'd like to elaborate on why it is helpful to focus on geometry in studying algebra. As MPW pointed out nicely in the comments, framing things in terms of geometry helps with intuition. That is, while you can and should develop intuition for algebra independently, geometry provides a convenient and deep source of intuition, taken from everyday life. This really helps in understanding the (generally quite abstract) concepts of Linear Algebra. It's always good to use previous knowledge to understand new material, and this is no exception. It's even valuable later when you have the algebraic intuition to see how the two match up and compliment each other.