What is Linear Algebra?

I’m done with Linear Algebra, and it was an interesting journey. Fun fact, I’ve been looking forward to this class since around 10th grade, when I first heard the topic mentioned somewhere (I don’t remember when exactly). And it took me 3 years to finally reach that goal and now as I reflect on linear algebra I gained an appreciation of all of math that came before it to culminate in one of the most difficult math courses during my life.

So the question that many may be wondering: What is linear algebra? Well, if you google that, the internet states, “Linear algebra is the branch of mathematics concerning linear equations” which isn’t particularly helpful. The way I see it, linear algebra is the study of all the math that came before it, but using the idea of matrices and spaces to describe the ideas we already know. For example, a system of equations solvable through the elimination method can now be solved using linear algebra through matrices. Another idea of this is vector spaces, which are actually just collections of objects that follow certain parameters.

Linear algebra is used to not only solve these, but understand different dimensions and spaces in mathematics. We can begin to understand higher level mathematics and its uses in physics and other sciences to model phenomenons. And of course, we cannot forget proofs which are such an integral part of linear algebra. Proving something whether its an equation or an identity to be true is huge in linear algebra, and is one of the most difficult parts to many students.

So if you couldn’t tell already, I quite enjoyed linear algebra. Although it was home to some of my lowest math exam scores in a long time, the ideas behind it were enjoyable and I felt that the wait was worth it. It’s a subject that is challenging in nature, but fun to understand.