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.
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Solution Summary
Parametrize the two halves of this line.
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