# Thread:

1. ## 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.

2. Originally Posted by JCIR
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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