The difference map : Cn Cn is defined as = S  I, where S
Question:
(a) Write down the matrix corresponding to A.
(b) Prove that the sampled exponential vectors w0, ...,wn1 from (5.90) form an eigenvector basis of ∆. What are the eigenvalues?
(c) Prove that K = ∆T ∆ has the same eigenvectors as ∆. What are its eigenvalues? Is K positive definite?
(d) According to Theorem 8.20 the eigenvectors of a symmetric matrix are real and orthogonal. Use this to explain the orthogonality of the sampled exponential vectors. But, why aren't they real?
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a b k S I k 1 e 2k i n k and so k is an eigenvector of with correspondin...View the full answer
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