Finding the eigenvalues of a complex matrix

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The discussion centers on finding eigenvalues of complex matrices, specifically questioning whether the explicit QR algorithm, which employs complex arithmetic, is applicable. The implicit QR algorithm, known for its effectiveness with real matrices, raises curiosity about its adaptation for complex cases. Participants consider the differences in handling complex numbers and the potential need for modifications to the algorithm. The conversation encourages sharing methods and insights to generalize the approach for complex matrices. Overall, the exploration aims to clarify the best practices for computing eigenvalues in this context.
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
 
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maybe if you explain what you do know, someone will see how to generalize it.
 
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