Let L be a Leslie matrix with a unique positive eigenvalue 1 . Show that if
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Let L be a Leslie matrix with a unique positive eigenvalue λ1. Show that if λ is any other (real or complex) eigenvalue of L, then |λ| ≤ λ1. [Write λ = r(cosθ + i sin θ) and substitute it into the equation g(λ) = 1, as in part (b) of Exercise 23. Use De Moivre’s Theorem and then take the real part of both sides. The Triangle Inequality should prove useful.]
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1 r 1 cos 0 i sin 0 r 1 since it is positive Let r cos i sin be some other ...View the full answer
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