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

Rajendra Bhatia; Tanvi Jain

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arXiv · 1803.04174

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

Rajendra Bhatia·Tanvi Jain

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Abstract

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.

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Rajendra Bhatia, Tanvi Jain. 2018-03-12. Positivity properties of the matrix $\left[(i+j)^{i+j}\right]$. https://arxiv.org/abs/1803.04174

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