Hi, there seems to be some eigenvector/eigenvalue rule I'm missing, because I don't understand the last steps in the solutions for problem 43 and 44 in the 2020 exam.
Many thanks for any clues :)
Edit: whoops I had just misremembered the definition of eigenvectors/-values as Aw = LambdaA , when in fact it is Aw = lambdaw. Hence the confusion. Sorry about the silly question
Ex. 2020 problem 43/44
Hi, there seems to be some eigenvector/eigenvalue rule I'm missing, because I don't understand the last steps in the solutions for problem 43 and 44 in the 2020 exam.
Many thanks for any clues :)
Edit: whoops I had just misremembered the definition of eigenvectors/-values as Aw = LambdaA , when in fact it is Aw = lambdaw. Hence the confusion. Sorry about the silly question
1
Hi,
Since, \(w_i\) is an eigenvector of matrix K with eigenvalue \(\rho_i\) by definition of eigenvector, \(K w_i = \rho_i w_i\) (see e.g. formal definition section in https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors )
(next time try to put the the the exercise & full solution in the screenshoot here, so it is faster to answer your question)
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