Inertia of the Matrix
نویسنده
چکیده
Let p1, . . . , pn be positive real numbers. It is well known that for every r < 0 the matrix [(pi + pj) r ] 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.
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