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absolute value accurate estimate application attains its maximum behavioral scientist Bodewig bound g chapter are summarized consider the matrix convergence of g converges monotonically cross-product terms derivation diagonal elements distinct eigenvalues easily computed Educational Psychology equal its minimum equation equivalent estimate of X estimate of X2 evaluating Factor Analysis following theorem g attains hence inequality interest lies larger in absolute largest eigenvalue limit Matrix Theory maximum value tr(A mean and variance minimized minimum value multivariate analysis n x n real necessary and sufficient necessary to show negative signs numerical example positive definite matrix positive semi-definite possible to obtain powering the matrix problem procedure is applied rational numbers remaining eigenvalues resulting expression sequence g significant digits simplifies sity of Wisconsin Statistical Variables sufficient condition symmetric matrix thesis tighter upper bound University of Wisconsin Wisconsin Library X2 based Z Z a2 zero