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    Let A be a matrix,  a real eigenvalue of A, and v the associated eigen-vector.

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    Let A be an nxn matrix, λ a real eigenvalue, v the associated eigenvector. Show that A^k v= λ^k v.
    Use this to show e^At v= e^λt v. Use this to show that the line through the origin consists of two solutions to x'=Ax.

    © BrainMass Inc. brainmass.com October 10, 2019, 1:40 am ad1c9bdddf
    https://brainmass.com/math/linear-algebra/real-eigenvalue-associated-eigen-vector-343970

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    Parametrize the two halves of this line.

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