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In Wooldridge's graduate book, 2nd edition, page 174, he states «The usual motivation for the GLS estimator is to transform a system of equations where the error has a nonscalar variance-covariance matrix into a system where the error vector has a scalar variance-covariance matrix.» What does he mean by this?

Does he mean that the resulting variance matrix will be diagonal? I've never head the expression «scalar variance-covariance matrix» before. Any help would be appreciated.

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