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

Let A be an n x n matrix with eigenvalue [tex]\lambda[/tex]. Prove that [tex]\lambda[/tex]^2 is an eigenvalue of A^2 and that if v is an eigenvector of A, then v is also an eigenvector for A^2.

2. Relevant equations

Av=[tex]\lambda[/tex]v

3. The attempt at a solution

Av=[tex]\lambda[/tex]v

(A*A)V=([tex]\lambda[/tex] * [tex]\lambda[/tex])v

so then v will be an eigenvector to A^2 when [tex]\lambda[/tex]^2

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

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: Linear Algebra Proof- Pleaseeeee help!

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