Wei Xie

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math.RA2026

Complete Bernstein functions and real powers of P-matrices

Wei Xie

We classify the nonzero complete Bernstein functions whose matrix functions preserve every real P-matrix in every order. They are precisely $f (z) = a + b z$ , with $a, b \geq 0$ and $a + b > 0$ ,…

math.RA2026

Exponent Profiles of Oscillatory Matrices under Matrix and Inverse Sparsity

Wei Xie

We classify the simultaneous half-bandwidths $p, q$ of a symmetric oscillatory matrix $A$ and its inverse. At order $n \geq 2$ , the possible pairs are $(1, n - 1)$ , $(n - 1, 1)$ , and all pai…

math.RA2026

Positive Eigenvalues of Hadamard Square Roots on Finite Abelian Groups

Wei Xie

For a finite abelian group $G$ , let $μ_{2} (G)$ be the minimum number of positive eigenvalues of an entrywise positive real symmetric group-circulant matrix whose entrywise square is…

math.RA2026

Entrywise Positivity Preservers on Green Matrices

Wei Xie

We classify the entrywise functions that preserve positive semidefiniteness on discrete Green matrices $G(p,q)=(p_{\min(i,j)}q_{\max(i,j)})$ with positive parameters, without req…