Mathematics, 28.05.2021 15:30 pedrojulianhdz2005

Suppose the matrix A is real but has complex eigenvalues. If the initial vector w in the power method is real, then all other quantities, including approximate eigenvalues, generated by the algorithm will be real. Hence if the eigenvalue of A of largest absolute value has nonzero imaginary part, then the power method will not converge to it. Can you explain this apparent paradox? (Hint: Can a real matrix have a complex eigenvalue li with nonzero imaginary part that satisfies [11] > [12] 2 ... 2 An]? Why or why not?)

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Suppose the matrix A is real but has complex eigenvalues. If the initial vector w in the power metho...