MathDB
FE Mn(R)->[n], inequality f(XY)≤min{f(X),f(Y)}

Source: SEEMOUS 2008 P3

June 17, 2021
inequalitiesfunctional equationfematrixlinear algebra

Problem Statement

Let Mn(R)\mathcal M_n(\mathbb R) denote the set of all real n×nn\times n matrices. Find all surjective functions f:Mn(R)→{0,1,…,n}f:\mathcal M_n(\mathbb R)\to\{0,1,\ldots,n\} which satisfy f(XY)≤min⁡{f(X),f(Y)}f(XY)\le\min\{f(X),f(Y)\}for all X,Y∈Mn(R)X,Y\in\mathcal M_n(\mathbb R).
Back to ProblemsView on AoPS