Eigenvalues & Eigenvectorshard
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Let λ\lambda be a simple eigenvalue of a matrix AA with right eigenvector xx (normalized to x2=1\|x\|_2=1) and left eigenvector yy (normalized to y2=1\|y\|_2=1). The condition number s(λ)1s(\lambda)^{-1} of the eigenvalue λ\lambda measures its sensitivity to perturbations. What is s(λ)s(\lambda)?