(a) Prove that if A is symmetric and tridiagonal, then all matrices Ak appearing in the Q...

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(a) Prove that if A is symmetric and tridiagonal, then all matrices Ak appearing in the Q R algorithm are also symmetric and tridiagonal. First prove symmetry.
(b) Is the result true if A is not symmetric-only tridiagonal?

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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 18, 2016 09:02 AM

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(a) Prove that if A is symmetric and tridiagonal, then all matrices Ak appearing in the Q...

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a By induction if A k Q k R k R T k Q T k A T k then since Q k is orthogonal A T k1 R k Q k T Q T k ...View the full answer

Applied Linear Algebra

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