Positivity of Hadamard powers of a few band matrices
نویسندگان
چکیده
Let $\mathbb{P}_G([0,\infty))$ and $\mathbb{P}_G^{'}([0,\infty))$ be the sets of positive semidefinite definite matrices order $n$, respectively, with nonnegative entries, where some positions zero entries are restricted by a simple graph $G$ $n$ vertices. It is proved that for connected $n\geq 3$, set powers preserving semidefiniteness on precisely same as definiteness $\mathbb{P}_G^{'}([0,\infty))$. In particular, this provides an explicit combinatorial description critical exponent definiteness, all chordal graphs. Using chain sequences, it Hadamard (semi) every tridiagonal matrix $r\geq 1$. The infinite divisibility studied. results special family pentadiagonal matrices.
منابع مشابه
Eigenvalues of Hadamard powers of large symmetric Pascal matrices
Let Sn be the positive real symmetric matrix of order n with (i, j ) entry equal to ( i + j − 2 j − 1 ) , and let x be a positive real number. Eigenvalues of the Hadamard (or entry wise) power S n are considered. In particular for k a positive integer, it is shown that both the Perron root and the trace of S n are approximately equal to 4 4k−1 ( 2n− 2 n− 1 )k . © 2005 Elsevier Inc. All rights r...
متن کاملOn Fractional Hadamard Powers of Positive Block Matrices
Entrywise powers of matrices have been well-studied in the literature, and have recently received renewed attention due to their application in the regularization of highdimensional correlation matrices. In this paper, we study powers of positive semidefinite block matrices (Hst) n s,t=1 where each block Hst is a complex m × m matrix. We first characterize the powers α ∈ R such that the blockwi...
متن کاملOn the powers of fuzzy neutrosophic soft matrices
In this paper, The powers of fuzzy neutrosophic soft square matrices (FNSSMs) under the operations $oplus(=max)$ and $otimes(=min)$ are studied. We show that the powers of a given FNSM stabilize if and only if its orbits stabilize for each starting fuzzy neutrosophic soft vector (FNSV) and prove a necessary and sufficient condition for this property using the associated graphs of the FNSM. ...
متن کاملPositivity and Conditional Positivity of Loewner Matrices
We give elementary proofs of the fact that the Loewner matrices [ f(pi)−f(pj) pi−pj ] corresponding to the function f(t) = t on (0,∞) are positive semidefinite, conditionally negative definite, and conditionally positive definite, for r in [0, 1], [1, 2], and [2, 3], respectively. We show that in contrast to the interval (0,∞) the Loewner matrices corresponding to an operator convex function on...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Electronic Journal of Linear Algebra
سال: 2022
ISSN: ['1081-3810', '1537-9582']
DOI: https://doi.org/10.13001/ela.2022.6553