(Yet another) Introduction to quaternions | lisyarus blog
There are thousands of articles about quaternions on the internet, but my social media said it won't hurt to have another one, so pretend you know nothing about quaternions, and let's roll.
Some people said that the biggest problem of all articles on quaternions is the abundance of formulas. Honestly, I have no idea how you could explain a mathematical object without formulas, though I will try to make them as innocent as possible. There will be a lot of algebra (but mostly very basic algebra), which we can't escape – quaternions are an algebraic object, after all. I'll try to derive all formulas except for a couple that are exceptionally long and boring.
Finally, a word about "understanding" quaternions. As von Neumann said, in maths you don't understand things, you just get used to them, and I tend to agree. With enough practice and exposure, you gradually become familiar with the subject and develop an internal intuition for it. When this happens repeatedly, at some point you say that you understand it. It might seem that a particular article, or book, or video made you finally understand, while in reality you probably already almost understood everything, and this last article just filled up one last bit of interwoven connections that you somehow missed, which made everything finally click and make sense.
Say, you're making a 3D game, and you need to work with rotating objects. Rotations are certain 3D transformations; it turns that they are always linear transformations, and can be expressed using a \(3\times 3\) matrix. Not every matrix represents a rotation, though; in fact, rotation matrices form a certain very special type of matrices. When you see such a matrix, say
