\[\newcommand{\u}[1]{\boldsymbol{\mathsf{#1}}} \renewcommand{\b}[1]{\boldsymbol{#1}} \newcommand{\t}[1]{\textsf{#1}} \newcommand{\m}[1]{\mathbb{#1}} \def\RR{\bf R} \def\bold#1{\bf #1} \def\mbf#1{\mathbf #1} \def\uv#1{\hat{\usf {#1}}} \def\dl#1{\underline{\underline{#1}}} \newcommand{\usf}[1]{\boldsymbol{\mathsf{#1}}} \def\bs#1{\usf #1}\]

In this section we are going to shown that for each rotation tensor $\boldsymbol{R}$ there exists a unit vector $\boldsymbol{a}$, which we will call $\boldsymbol{R}$’s axis of rotation such that

$\boldsymbol{R}\boldsymbol{a}=\boldsymbol{a}$

That is, we are saying that there is a special vector corresponding to the rotation tensor that does not move by its action.