Show that for a non-Hermitian matrix A C^( mm), the Rayleigh quotient r(x) gives an eigenvalue
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Question:
Show that for a non-Hermitian matrix A ∈ C^( m×m), the Rayleigh quotient r(x) gives an eigenvalue estimate whose accuracy is generally linear, not quadratic. Explain what convergence rate this suggests for the Rayleigh quotient iteration applied to non-Hermitian matrices.
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