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

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