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First order differential corrections in the eigenvalue problem Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/2514np659

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  • Let A be an n x n real, symmetric matrix with distinct characteristic values λ₁, λ₂,...,λɴ. Then there exists an orthogonal matrix P such that PAPᵀ = Λ = (λi). Given a small symmetric change, ∆A, in the matrix A, we can calculate the resulting changes, ∆P, and ∆Λ, in P and ∧ respectively. We next assume that the change in A is dependent on time t. In particular, we assume that A(t) is a differentiable function of t. Then, if A₀ A(0) has distinct characteristic values, we show that for sufficiently small t, P and Λ are differentiable functions of t, and that A(t) also has distinct characteristic values.
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2014-03-05T19:32:56Z (GMT) No. of bitstreams: 1 AkersDavidW1969.pdf: 159345 bytes, checksum: 9b21670cd65c8807bea08190fd7718a9 (MD5)
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  • description.provenance : Approved for entry into archive by Patricia Black(patricia.black@oregonstate.edu) on 2014-03-06T20:49:44Z (GMT) No. of bitstreams: 1 AkersDavidW1969.pdf: 159345 bytes, checksum: 9b21670cd65c8807bea08190fd7718a9 (MD5)
  • description.provenance : Made available in DSpace on 2014-03-06T20:49:44Z (GMT). No. of bitstreams: 1 AkersDavidW1969.pdf: 159345 bytes, checksum: 9b21670cd65c8807bea08190fd7718a9 (MD5) Previous issue date: 1969-04-24

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