(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose A is an n x n matrix with the property that A^{2}=A

a. Show that if λ is an eigenvalue of A, then λ=0 or λ=1

b. Prove that A is diagonalizable.

2. Relevant equations

Av=λv (v : eigenvector)

3. The attempt at a solution

solution for a.

A^{2}v=A(Av)=A(λv)=λ(Av)=λλv. also, Av=λv, therefore, λ^{2}v=λv

=> (λ^{2}-λ)v=0. So, λ=0 or λ=1.

I want you to check if this sounds right. If you see any errors, let me know. Now I'm working on the b part, but im pretty much stuck. I will post up when I find something. Thanks in advance

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Eigenvalue/Eigenvector problem. Check my solution please.

**Physics Forums | Science Articles, Homework Help, Discussion**