Let u1,...,un be an orthonormal basis of Rn. Prove that it forms an eigenvector basis for some

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Let u1,...,un be an orthonormal basis of Rn. Prove that it forms an eigenvector basis for some symmetric n × n matrix A. Can you characterize all such matrices?
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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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