Theoretical Statistics and Mathematics Unit, ISI Delhi

Positivity properties of the matrix $\left[(i+j)^{i+j}\right]$

by Rajendra Bhatia and Tanvi Jain

Let $p_1 < p_2 < \cdots < p_n$ be positive real numbers. It is shown that the matrix whose $i,j$ entry is $(p_i+p_j)^{p_i+p_j}$ is infinitely divisible, nonsingular and totally positive.

isid/ms/2015/11 [fulltext]

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