Let L be a Leslie matrix with a unique positive eigenvalue 1 . Show that if is any other (real or complex) eigenvalue

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.]