In this post we study projective representations of $SO(3)$, although we will make more use of $SU(2)$. At the end of this post we reach the conclusion that one will think about polynomials with odd or even terms. Projective representations have its own significance in physics although the room of this post is too small to contain it. Nevertheless, the reader is invited to use linear algebra much more extensively with a taste of modern physics in this post.

In this post we follow the step of Fulton-Harris to classify all irreducible representations of $GL_2(\mathbb{F}_q)$. A character table is added at the end.

In this post, irreducible representations of $SO(3)$ are studied, with much more extensive applications of linear algebra.

$SU(2)$ has a lot of interesting mathematical and physical properties. In this post we study its irreducible representations in a mathematician's way.

I think it’s quite often that, when you are learning mathematics beyond linear algebra, you are stuck at some linear algebra problems, but you haven’t learnt that systematically before although you wish you had. In this blog post we will go through some content that is not universally taught but quite often used in further mathematics. But this blog post does not serve as a piece of textbook. If you find some interesting topics, you know what document you should read later, and study it later.

This post is still on progress, neither is it finished nor polished properly. For the coming days there will be new contents, untill this line is deleted. What I’m planning to add at this moment:

• Transpose is not just about changing indices of its components.
• Norm and topology in vector spaces
• Representing groups using matrices