# Definition A rotation in $n$ dimensions is any [[linear operator]] $R$ which can be *obtained continuously from the identity* and takes [[Orthogonality|orthonormal]] [[basis|bases]] to orthonormal base. That is, given an orthonormal basis $\{\pmb{e}_i\}_{i = 1\ldots n}$ then the rotated basis $\{R\pmb{e}_i\}_{i = 1\ldots n}$ is also orthonormal. This condition is equivalent to saying that $R$ is a [[Special Orthogonal Group|special orthogonal]] operator, i.e., $R \in SO(n)$