In this post we show that $SL(2,\mathbb{R})$ can be identified as the inside of a solid torus and see what we can learn from it.

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, 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.