![]() "Reflection Groups, Generalized Schur Functions, and the Geometry of Majorization." Ann. When $G$ is the permutation group $\mathscr_n$, and has applications to probability inequalities arising in multivariate statistical analysis. A reflection is an example of a transformation. A real-valued function $f$ on $R^n$ is called $G$-monotone (decreasing) if $f(y) \geqq f(x)$ whenever $y \precsim x$, i.e., whenever $y \in C(x)$, where $C(x)$ is the convex hull of the $G$-orbit of $x$. In geometry, a transformation is an operation that moves, flips, or changes a shape to create a new shape. ![]() ![]() Let $G$ be a closed subgroup of the orthogonal group $O(n)$ acting on $R^n$. Want to join the conversation Sort by: Top Voted MFZ 8 years ago Is a translation and a transformation the same thing 11 comments ( 76 votes) Upvote Downvote Flag POTATO :) 4 years ago No.A transformation includes rotations, reflection, and translations.
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