Title: Existence of an A-optimal model for a regression experiment
Abstract: The existence of certain A-optimal models for a regression experiment is equivalent to the solvability of certain matrix equations. It is proved that for any m × m matrix V (over the real field), there exists an orthogonal matrix Q such that QVQ′ has equal diagonal elements. This result is used to solve the equations mentioned above. The connection of this result to Hadamard matrices is discussed.