A class of positive semidefinite matrices (Q1104382)

It is a known fact that, given a positive definite matrix \(y_{ij}\), the ``standardized'' matrix \(y_{ij}(y_{ii}y_{jj})^{-}\) is again positive definite. The authors investigate more general standardization methods of the form \(a_{ij}(\alpha)y_{ij}\) where \(\alpha\) is a positive number and \(a_{ij}(\alpha)=(\phi (x_ i,\alpha)+\phi (x_ j,\alpha))^{-}.\) Positive definiteness and positive semidefiniteness is preserved under fairly general conditions.