  General ridge estimators are typical linear estimators in a general linear
model. The class of them include some shrinkage estimators in addition to
classical linear unbiased estimators such as the ordinary least squares
estimator and the weighted least squares estimator. We derive necessary and
sufficient conditions under which two general ridge estimators coincide. In
particular, two noteworthy conditions are added to those from previous studies.
The first condition is given as a seemingly column space relationship to the
covariance matrix of the error term, and the second one is based on the biases
of general ridge estimators. Another problem studied in this paper is to derive
an equivalence condition such that equality between two residual sums of
squares holds when general ridge estimators are considered.
