## Tables from this paper

## 12 Citations

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To every finite metric space X, including all connected unweighted graphs with the minimum edge-distance metric, we attach an invariant that we call its blowup-polynomial pX({nx : x ∈ X}). This is…

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This work considers the refined problem of characterizing the set of entrywise powers preserving positivity for matrices with a zero pattern encoded by G, and studies how the geometry of $G$ influences the set $\mathcal{H}_G$.

Positivity preservers forbidden to operate on diagonal blocks

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The question of which functions acting entrywise preserve positive semidefiniteness has a long history, beginning with the Schur product theorem [Crelle 1911], which implies that absolutely monotonic…

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We prove the converse to a result of Karlin [Trans. AMS 1964], and also strengthen his result and two results of Schoenberg [Ann. of Math. 1955]. One of the latter results concerns zeros of Laplace…

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For every finite simple connected graph $G = (V,E)$, we introduce an invariant, its blowup-polynomial $p_G(\{ n_v : v \in V \})$. This is obtained by dividing the determinant of the distance matrix…

Positivity of Hadamard powers of tridiagonal matrices

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Let Mn(R) denotes the set of all n× n matrices over R. A matrix A ∈ Mn(R) is called nonnegative if all its entries are nonnegative. In this paper, every matrix belongs to Mn(R), and is nonnegative…

Positivity of Hadamard powers of a few band matrices

- MathematicsThe Electronic Journal of Linear Algebra
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Let $\mathbb{P}_G([0,\infty))$ and $\mathbb{P}_G^{'}([0,\infty))$ be the sets of positive semidefinite and positive definite matrices of order $n$, respectively, with nonnegative entries, where some…

Post-composition transforms of totally positive kernels

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Author(s): Belton, Alexander; Guillot, Dominique; Khare, Apoorva; Putinar, Mihai | Abstract: The composition operators preserving total non-negativity and total positivity for various classes of…

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This survey contains a selection of topics unified by the concept of positive semidefiniteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks)…

Totally positive kernels, Polya frequency functions, and their transforms

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The composition operators preserving total non-negativity and total positivity for various classes of kernels are classified, following three themes. Letting a function act by post composition on…

## References

SHOWING 1-10 OF 51 REFERENCES

Complete characterization of Hadamard powers preserving Loewner positivity, monotonicity, and convexity

- Mathematics
- 2015

Preserving positivity for matrices with sparsity constraints

- Mathematics
- 2014

Functions preserving Loewner positivity when applied entrywise to positive semidefinite matrices have been widely studied in the literature. Following the work of Schoenberg [Duke Math. J. 9], Rudin…

Preserving positivity for rank-constrained matrices

- Mathematics
- 2017

Entrywise functions preserving the cone of positive semidefinite matrices have been studied by many authors, most notably by Schoenberg [Duke Math. J. 9, 1942] and Rudin [Duke Math. J. 26, 1959].…

Functions preserving positive definiteness for sparse matrices

- Mathematics
- 2012

We consider the problem of characterizing entrywise functions that preserve the cone of positive definite matrices when applied to every off-diagonal element. Our results extend theorems of…

On a Parametrization of Positive Semidefinite Matrices with Zeros

- MathematicsSIAM J. Matrix Anal. Appl.
- 2010

This work gives a semialgebraic description of the images of the parametrizations for chordless cycles and is motivated by the fact that the considered maps correspond to Gaussian statistical models with hidden variables.

Functions operating on positive definite matrices and a theorem of Schoenberg

- Mathematics
- 1978

We prove that the set of all functions/: [-1, l]-»[-l, 1] operating on real positive definite matrices and normalized such that/(l) = 1, is a Bauer simplex, and we identify its extreme points. As an…

The theory of infinitely divisible matrices and kernels

- Mathematics
- 1969

when he showed recently that the Green's function for Laplace's equation is, under certain conditions, an infinitely divisible kernel. In this paper we shall develop a general theory of infinitely…

Extreme points in convex sets of symmetric matrices

- Mathematics
- 1985

This paper deals with the following problem: What are the extreme points of a convex set K of n X n matrices, which is the intersection of the set S" of symmetric matrices of nonnegative type, with…