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Consider an N x N matrix A  with N orthonormal eigenvectors xi such that Axi = λi xi  , where the λi is the eigenvalue corrosponding to eigenvector xi . It can be shown that such a matrix A has an expansion of the form : (see image) ii) Using the result for A  show that the  N x N identify matrix can be written as : i = (see image)

Consider an N x N matrix A  with N orthonormal eigenvectors xi such that Axi = λi xi  , where the λi is the eigenvalue corrosponding to eigenvector xi . It can be shown that such a matrix A has an expansion of the form : (see image) ii) Using the result for A  show that the  N x N identify matrix can be written as : i = (see image)

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter58: Achievement Review—section Five
Section: Chapter Questions
Problem 30AR: Determine dimension x to 3 decimal places.
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b) Consider an N x N matrix A  with N orthonormal eigenvectors xi such that Axi = λi xi  , where the λi is the eigenvalue corrosponding to eigenvector xi . It can be shown that such a matrix A has an expansion of the form : (see image)

ii) Using the result for A  show that the  N x N identify matrix can be written as : i = (see image)

N N A = Σ^{x^{x^| = Σλιπ (x). Α = i=1 i=1 Α = [0 1 07 1 0 1 010 N 1=2x(x). i=1
Transcribed Image Text:N N A = Σ^{x^{x^| = Σλιπ (x). Α = i=1 i=1 Α = [0 1 07 1 0 1 010 N 1=2x(x). i=1
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