The question

If A is a matrix with eigenvectorvand corresponding eigenvalue $\displaystyle \lambda$ prove thatvis also an eigenvector of $\displaystyle A^2$ and find the corresponding eigenvalue.

I'm not sure how to attempt this. Any hints?

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- Sep 25th 2011, 04:48 AMGlitchProve matrix A has same eigenvector as A^2
**The question**

If A is a matrix with eigenvector**v**and corresponding eigenvalue $\displaystyle \lambda$ prove that**v**is also an eigenvector of $\displaystyle A^2$ and find the corresponding eigenvalue.

I'm not sure how to attempt this. Any hints? - Sep 25th 2011, 05:04 AMDevenoRe: Prove matrix A has same eigenvector as A^2
Av = λv.

so A^2(v) = A(λv) = λ(Av) = .....?