MathDB
IMC 1996 Problem 3

Source: IMC 1996

March 5, 2021
vectorlinear algebra

Problem Statement

The linear operator AA on a finite-dimensional vector space VV is called an involution if A2=IA^{2}=I, where II is the identity operator. Let dimV=n\dim V=n. i) Prove that for every involution AA on VV, there exists a basis of VV consisting of eigenvectors of AA. ii) Find the maximal number of distinct pairwise commuting involutions on VV.