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Homework Statement
Let Q be an orthogonal matrix with an eigenvalue [itex]λ_{1}[/itex] = 1 and let x be an eigenvector belonging to [itex]λ_{1}[/itex]. Show that x is also an eigenvector of [itex]Q^{T}[/itex].
Homework Equations
Qx = λx where x [itex]\neq[/itex] 0
The Attempt at a Solution
[itex]Qx_{1} = x_{1}[/itex] for some vector [itex]x_{1}[/itex]
[itex](Qx_{1})^{T} = x_{1}^{T}Q^{T}[/itex]
I'm kind of stuck with how to start this problem, as I'm not sure what I've done is even starting down the right path. Can anyone give me a nudge in the right direction?