(a) Prove that if Q is an orthogonal matrix, then ||Qx|| = ||x|| for any vector x...

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(a) Prove that if Q is an orthogonal matrix, then ||Qx|| = ||x|| for any vector x ∊ Rn, where ||∙|| denotes the standard Euclidean norm.
(b) Prove the converse: if ||(Qx|| = ||x|| for all x ∊ Rn, then Q is an orthogonal matrix.

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Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

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Question Posted: Jun 17, 2016 08:49 AM

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(a) Prove that if Q is an orthogonal matrix, then ||Qx|| = ||x|| for any vector x...

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a Qx 2 Qx T Qx x T Q T Qx x T I x x T x ...View the full answer

Applied Linear Algebra

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