IMC 1996 Problem 3
Source: IMC 1996
March 5, 2021
vectorlinear algebra
Problem Statement
The linear operator on a finite-dimensional vector space is called an involution if
, where is the identity operator. Let .
i) Prove that for every involution on , there exists a basis of consisting of eigenvectors
of .
ii) Find the maximal number of distinct pairwise commuting involutions on .