Let p() = (-1 )n(n - n-1n-1 -....- 1 - o) he a polynomial of degree n
Question:
(a) Show that if λi, is a root of p(λ) = 0 then λi is an elgenvalue of C with eigenvector x = (λin-1,,λ in-2...... λi,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 is called the companion matrix of p(λ).
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a If i is a root of p then n i a n1 n1 i a 1 i a 0 Thus if x i n1 i n2 2 i i 1 T then Cx ...View the full answer
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