Prove that if v is an eigenvector of A with eigenvalue and w is an eigenvector

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Prove that if v is an eigenvector of A with eigenvalue λ and w is an eigenvector of Awith a different eigenvalue μ ≠ λ, then v and w are orthogonal vectors with respect to the dot product. Illustrate this result when


(i)


image


(ii)


image

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Applied Linear Algebra

ISBN: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

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