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Mathematics > Classical Analysis and ODEs

Title: Hadamard powers of some positive matrices

Authors: Tanvi Jain
Abstract: 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 $r<n-2$ that is not an integer, and $\begin{bmatrix}|\cos((i-j)\pi/n)|^r\end{bmatrix}$ is positive semidefinite for every odd integer $n\ge 3$ and $n-3\le r<n-2.$
Subjects: Classical Analysis and ODEs (math.CA); Functional Analysis (math.FA)
Journal reference: Linear Algebra and its Applications, 528, (2017) 147-158
Cite as: arXiv:1803.06803 [math.CA]
  (or arXiv:1803.06803v1 [math.CA] for this version)

Submission history

From: Tanvi Jain [view email]
[v1] Mon, 19 Mar 2018 05:04:41 GMT (10kb)