What is linear algebra?

[jewish_scientist]

Considering I studied lines and their equations in middle school and a prerequisite to my college's linear algebra class is Calculus I, I am going to go out on a limb here and guess that linear algebra is not what I think it is.

[Demki]

Linear algebra is less about "lines and their equals" and more about vector spaces, and linear functions between them.
Linear functions are functions that preserve vector addition and multiplication by a scalar.
In linear algebra you'll learn what a vector space is, and you'll learn about matrices and operations on matrices, among other things.

Here are a few videos on linear algebra by 3blue1brown(Grant Sanderson), which explain some of the ideas behind linear algebra using appropriate visuals. They are not a replacement for actually learning linear algebra.

[Thesh]

It is related, however. It pretty much all starts with learning to solve systems of linear equations using matrices, and expands from there. So while it quickly goes into vector spaces, it is really a continuation of the linear algebra you learned in middle school.

[Eebster the Great]

I failed to appreciate how complicated simple concepts can become until I learned how to prove that 1+1=2. (This isn't a remotely complicated proof in any system, as far as I know, but it is still substantially more complicated than I expected it to be.) Linear algebra at its very heart is sort of what you expect it to be, but its complexity might still surprise you.