Our final application of matrix multiplication will be solving derivatives and integrals—and notably finding an easy solution to a particular integral that's famously difficult to evaluate! This is our final look at what doors matrix multiplication can open with your programming, however there's an enormously diverse world of other applications that you can pursue in your programming career.

Task

Now that you've seen just a few diverse examples of matrix multiplication in action, your task is to return to the material from chapter 2, rewatch the video and look over the diagram and examples provided, and see if you can get a more complete understanding of the concepts and matrix multiplication—and what strange doors it can open for your programming future.

Tips for getting the chapter 2 content down:

• It's important to keep confident. Keep crazy confident, in fact. Crash into new territory like the tide, just to the point where you start to feel truly out of your element, then retreat back to your comfort zone, reestablish and strengthen those foundations, and use that force to crash further in;

• It helps to look over the examples provided in the chapter, to really see that their bark is much worse than their bite;

• The definitions are intentionally abstract, to maximize their possible applications. So if they seem a bit weird, you're not wrong! They belong to a well-established branch of mathematics known as abstract algebra, where the approach is more like seeing the forest through the trees. Plus side: no arithmetic required;

• It may seem like you can just define any old thing. That's true! But only what's useful survives;

• There are worlds of resources online, videos, books, websites, etc., covering each definition and concept. It's good to find a resource that you find communicates well, and inspires your confidence and interest—there's no better criteria;

• While learning is always good, you don't need to go out and spend eons learning mathematics (there's better things to do with your time and career!). The cursory overview we give in chapter 2 was carefully constructed to simultaneously constitute formal proof of all the principles needed. So you can bet your money on it, and pick up additional details only as they appeal to you.