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What are condition numbers and why are they important?

condition Numbers
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What are condition numbers and why are they important?

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The ratio of the largest eigenvalue to the smallest eigenvalue, referred to as the condition number, is a measure of ill-conditioning. Eigenvalues are generated by NONMEM when the PRINT=E argument is used in the $COVARIANCE record. A condition number exceeding 1 000 is indicative of severe ill-conditioning (Montgomery DC, Peck EA. Introduction to Linear Regression Analysis. Wiley, NY, 1982, pp. 301-302). Thanks to William Bachman for this definition, which I’ve shamelessly stolen.

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