  In a general linear model, this paper derives a necessary and sufficient
condition under which two general ridge estimators coincide with each other.
The condition is given as a structure of the dispersion matrix of the error
term. Since the class of estimators considered here contains linear unbiased
estimators such as the ordinary least squares estimator and the best linear
unbiased estimator, our result can be viewed as a generalization of the
well-known theorems on the equality between these two estimators, which have
been fully studied in the literature. Two related problems are also considered:
equality between two residual sums of squares, and classification of dispersion
matrices by a perturbation approach.
