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#### Residual Vectors.

Let denote a computed eigenvalue of , and let be its corresponding computed eigenvector, i.e.,

Sometimes, its corresponding left computed eigenvector is also available:

For simplicity, we normalize the computed eigenvectors so that and . The residual vectors corresponding to the computed eigenvalue and right and left computed eigenvectors and are defined as

respectively. We are interested in knowing the accuracy of the computed eigenvalue and eigenvectors and in terms of these residuals.

Susan Blackford 2000-11-20