Let p(λ)=(-1)^n(λ^n-a_n-1 λ^n-1-⋯-a_1 λ-…

Let p(λ)=(-1)^n(λ^n-a_n-1 λ^n-1-⋯-a_1 λ-a_0) be a polynomial of degree n ≥1, and let
C=([ a_n-1 amp; a_n-2 amp; ⋯ amp; a_1 amp; a_0; 1 amp; 0 amp; ⋯ amp; 0 amp; 0; 0 amp; 1 amp; ⋯ amp; 0 amp; 0; ⋮ amp; amp; amp;; 0 amp; 0 amp; ⋯ amp; 1 amp; 0 ])
(a) Show that if λ_i is a root of p(λ)=0, then λ_i is an eigenvalue of C with eigenvector 𝐱= (λ_i^n-1, λ_i^n-2, …, λ_i, 1)^T (b) Use part (a) to show that if p(λ) has n distinct roots then p(λ) is the characteristic polynomial of C The matrix C is called the companion matrix of p(λ)

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Видео Let p(λ)=(-1)^n(λ^n-a_n-1 λ^n-1-⋯-a_1 λ-… канала Thomas Carlson