The Condition Number <Back to Last Page>     <Full Glossary>

Definition of The Condition Number: The condition number is a measure of how close a matrix is to being singular. Relevant in estimation if the matrix of regressors is nearly singular the data are nearly collinear and (a) it will be hard to make an accurate or precise inverse, (b) a linear regression will have large standard errors.

The condition number is computed from the characteristic roots or eigenvalues of the matrix. If the largest characteristic root is denoted L and the smallest characteristic root is S (both being presumed to be positive here, that is, the matrix being diagnosed is presumed to be positive definite), then the condition number is:

gamma = (L/S)^.5

Values larger than 20, according to Greene (93), are observed if and only if the matrix is 'nearly singular'. (Econterms)

Terms related to The Condition Number:

• Eigenvalue
• Characteristic root

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