Theoretical Statistics and Mathematics Unit, ISI Delhi

Inertia of the matrix $[(p_i+p_j)^r]$}

by Rajendra Bhatia and Tanvi Jain

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.

isid/ms/2013/12 [fulltext]

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