Finding the eigenvalues of a complex matrix

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SUMMARY

The discussion focuses on finding the eigenvalues of complex matrices using the QR algorithm. The implicit QR algorithm, which employs the Francis QR step, is effective for real square matrices. Participants suggest that the explicit version of the QR algorithm can be adapted for complex matrices by utilizing complex arithmetic. This adaptation allows for the computation of eigenvalues in a broader context, enhancing the versatility of the QR algorithm.

PREREQUISITES
  • Understanding of the QR algorithm and its applications
  • Familiarity with complex numbers and complex arithmetic
  • Knowledge of eigenvalues and eigenvectors in linear algebra
  • Experience with matrix operations and properties
NEXT STEPS
  • Research the explicit QR algorithm for complex matrices
  • Study the Francis QR step and its implementation
  • Explore numerical methods for eigenvalue computation
  • Examine case studies of eigenvalue problems in complex systems
USEFUL FOR

Mathematicians, data scientists, and engineers working with linear algebra and complex systems will benefit from this discussion, particularly those focused on eigenvalue computations in advanced applications.

jezza10181
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Hi,

I am aware of the implicit QR algorithm, which utilises the 'Francis QR step' to find the eigenvalues of a real, square matrix.

But, how would one find the eigenvalues of a complex matrix? Would the 'explicit' version of the QR algorithm be used here, using complex arithmetic?

Thanks
 
Physics news on Phys.org
maybe if you explain what you do know, someone will see how to generalize it.
 

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