Abstract
A matrix [ a ij (α) x ij ] is shown to be positive semidefinite or positive definite if the matrix [ x ij ] is positive semidefinite or positive definite and a ij (α) belongs to a large class of functions of α. This class includes the reciprocals of the αth mean values of x ii and x jj in the cases where x ii , x jj , and α are all positive.
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