For the past few months I have been learning about the fundamental concepts of linear algebra in order to make my life as an aspiring game developer easier. Whilst working on the topic of null space, I've come across the following definition:
The null space of an $m × n$ matrix $A$ is the set of all solutions of the homogeneous equation $Ax = 0$.
As I looked into the term 'homogeneous equation', I realised that this was a concept that I am completely unfamiliar with, and most likely not one that can be understood quickly.
As I peer into the rabbit hole, I see that:
1). I order to understand what is meant by 'homogeneous equation', I will probably have to understand differential calculus.
2). In order to understand differential calculus I will probably have to have at least a basic grasp of calculus.
3). In order to have a basic grasp of calculus I will probably have to understand mathematical functions.
I haven't spent any time learning about any of the aforementioned topics.
The problem I have now is that, in order to understand the definition of null space properly, I will probably have to go through a multiple-month-detour around the topics that lead into homogeneous equations.
So my question to the reader is; is this worth it? For somebody who is learning about linear algebra for the purposes of game programming, is it worth spending multiple months learning about these topics, and if so what would be a good starting point? Or, would I be better off grazing over the idea of 'homogeneous equations'?