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  1. #1
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    Linear Algebra help

    Let T e an invertible linear operator. Prove that a scalar Lamda is an eigenvalue of T. if and only if the inverse of lamda is and eigen value of T^-1.
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    Quote Originally Posted by JCIR View Post
    Let T e an invertible linear operator. Prove that a scalar Lamda is an eigenvalue of T. if and only if the inverse of lamda is and eigen value of T^-1.
    Could it be this simple?:

    T^{-1} v = \frac{1}{\lambda} v \Rightarrow T \, T^{-1} v = \frac{1}{\lambda} T \, v \Rightarrow \lambda v = T \, v.


    T \, w = \lambda w \Rightarrow T^{-1} T \, w = T^{-1}\lambda \, w \Rightarrow \frac{1}{\lambda} \, w = T^{-1} w.

    Details and justifications left to you.
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