Theoretical Statistics and Mathematics Unit, ISI Delhi

Hadamard powers of some positive matrices

by Tanvi Jain

Positivity properties of the Hadamard powers of the matrix
$\begin{bmatrix}1+x_ix_j\end{bmatrix}$ for distinct positive real numbers
$x_1,\ldots,x_n$
and the matrix $\begin{bmatrix}|\cos((i-j)\pi/n)|\end{bmatrix}$ are studied.
In particular, it is shown that $\begin{bmatrix}(1+x_ix_j)^r\end{bmatrix}$
is not positive semidefinite for any positive real number $r

isid/ms/2018/03 [fulltext]

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