Unitary equivalence to a complex symmetric matrix: An algorithm

@article{Tener2008UnitaryET,
  title={Unitary equivalence to a complex symmetric matrix: An algorithm},
  author={James E. Tener},
  journal={Journal of Mathematical Analysis and Applications},
  year={2008},
  volume={341},
  pages={640-648}
}
  • James E. Tener
  • Published 1 May 2008
  • Mathematics
  • Journal of Mathematical Analysis and Applications
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25 Citations
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25 Citations

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A new fast and efficient algorithm for computing the eigenvalues and eigenvectors of large-size nondefective complex symmetric matrices is presented, similiar to the QR (QL) algorithm for complex Hermitian matrices, but it uses complex orthogonal (not unitary) transformations.
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It is shown that a contraction on a Hilbert space is complex sym- metric if and only if the values of its characteristic function are all symmetric with respect to a fixed conjugation. Applications…
Some new classes of complex symmetric operators
We say that an operator T E B(H) is complex symmetric if there exists a conjugate-linear, isometric involution C: ℌ→ℌ so that T = CT * C. We prove that binormal operators, operators that are…
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A bounded linear operator T on a complex Hilbert space H is called complex symmetric if T = CT*C, where C is a conjugation (an isometric, antilinear involution of H). We prove that T = CJ\T|, where J…
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Norm estimates of complex symmetric operators applied to quantum systems
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Truncated Toeplitz Operators on Finite Dimensional Spaces
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