Finite-sample analysis of rotation operator under $l_2$ norm and $l_{\mathrm{\infty }}$ norm

In this article, we consider a special operator called the two-dimensional rotation operator and analyze its convergence and finite-sample bounds under the $l_2$ norm and $l_{\mathrm{\infty }}$ norm with constant step size. We then consider the same problem with stochastic noise with affine variance. Furthermore, simulations are provided to illustrate our results. Finally, we conclude this article by proposing some possible future extensions.