MathDB

Bijection

Source: Iranian National Olympiad (3rd Round) 2006

September 21, 2006

geometrygeometric transformationvectorparallelograminductionlinear algebralinear algebra unsolved

Problem Statement

f: \mathbb R^{n}\longrightarrow\mathbb R^{n}

is a bijective map, that Image of every

n-1

-dimensional affine space is a

n-1

-dimensional affine space. 1) Prove that Image of every line is a line. 2) Prove that

f

is an affine map. (i.e.

f=goh

that

g

is a translation and

h

is a linear map.)