Publications and Preprints

Let $p_1, \ldots, p_n$ be positive real numbers. It is well known that for every $r<0$ the matrix $\left [\left (p_i+p_j \right )^r\right ]$ is positive definite. Our main theorem gives a count of the number of positive and negative eigenvalues of this matrix when $r>0.$ Connections with some other matrices that arise in Loewner's theory of operator monotone functions and in the theory of spline interpolation are discussed.