查看更多>>摘要：We generalize the concept of Pascal matrices to matrices associated with sets of points R subset of Z(>=)(0)(n) by considering multidimensional binomial coefficients as entries. We study their properties and prove that the infinite matrix associated with the set R = Z(>=)(0)(n) is in fact an element of the multivariate Riordan group. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Let H be a complex separable Hilbert space with dim H >= 3 and B(H) the Banach algebra of all bounded linear operators on H. Denote by w(A) the numerical radius of a bounded linear operator A is an element of B(H) and AB - BA* the skew Lie product of two operators A, B is an element of B(H). In this paper, it is shown that, if a surjective map Phi : B(H) -> B(H) satisfies w(AB-BA*) = w(Phi(A)Phi(B) - Phi(B)Phi(A)*) for all A, B is an element of B(H), then there exist a unitary operator U is an element of B(H), a functional h : B(H) -> {-1, 1} and a subset S subset of B(H) consisting of some normal operators such that Phi(A) = h(A)U AU* if A is an element of Phi(H) \ S and (I)(A) = Phi(A)U A*U* if A is an element of S. Particularly, if dim H < infinity, a complete characterization of S can be obtained. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The Perron value rho(T) of a rooted tree T has a central role in the study of the algebraic connectivity and characteristic set, and it can be considered a weight of spectral nature for T. A different, combinatorial weight notion for T - the moment mu(T) - emerges from the analysis of Kemeny's constant in the context of random walks on graphs. In the present work, we compare these two weight concepts showing that mu(T) is "almost" an upper bound for rho(T) and the ratio mu(T)/rho(T) is unbounded but at most linear in the order of T. Furthermore, we introduce two new objects associated with T - the Perron entropy and the neckbottle matrix - and we investigate how different operations on the set of rooted trees affect the Perron value and the moment. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we determine the underlying graphs of the mixed graphs with smallest Hermitian eigenvalue greater than -root 3. Furthermore, we characterize all mixed graphs on n >= 11 vertices with smallest Hermitian eigenvalue greater than -root 3. The mixed graphs on n <= 10 vertices with smallest Hermitian eigenvalue greater than -root 3 could be also obtained easily with the help of computer because their underlying graphs are determined. Roughly speaking, we completely determine the mixed graphs with smallest Hermitian eigenvalue greater than -root 3. (C) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：A celebrated result of Karpelevic describes circle minus(n), the collection of all eigenvalues arising from the stochastic matrices of order n. The boundary of circle minus(n) consists of roots of certain one-parameter families of polynomials, and those polynomials are naturally associated with the so-called reduced Ito polynomials of Types 0, I, II and III. In this paper we explicitly characterise all n x n stochastic matrices whose characteristic polynomials are of Type 0 or Type I, and all sparsest stochastic matrices of order n whose characteristic polynomials are of Type II or Type III. The results provide insights into the structure of stochastic matrices having extreme eigenvalues. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：In this paper, we consider the properties of operator parallel sum under weaker assumptions, and extend some important results of parallel sum to the case where the operator range 7Z(A + B) is not necessarily closed. Using Douglas theorem, the necessary conditions are given such that CA and CB are weakly parallel summable, and the weak parallel sum CA : CB = C(A : B) is further obtained. Under the restriction of 7Z(A) and 7Z(B) being closed, the several equivalent forms of A : B are given. Finally, the necessary and sufficient condition for C : (-A) to be the solution of A : X = C is provided, the necessary and sufficient conditions of A : B = (A dagger + B dagger) dagger are obtained and the new proof is given. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We establish Hadamard-type inequalities for a class of symmetric matrices called k-positive matrices for which the m-th elementary symmetric functions of their eigenvalues are positive for all m <= k. These matrices arise naturally in the study of k-Hessian equations in Partial Differential Equations. For each k-positive matrix, we show that the sum of its principal minors of size k is not larger than the k-th elementary symmetric function of their diagonal entries. The case k = n corresponds to the classical Hadamard inequality for positive definite matrices. Some consequences are also obtained.(c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：Let X be a finite connected poset, F a field and I(X, F) the incidence algebra of X over F. We describe the bijective linear idempotent preservers phi : I(X, F) -> I(X, F). Namely, we prove that, whenever char(F) 2, phi is either an automorphism or an anti-automorphism of I(X, F). If char(F) = 2 and |F| > 2, then phi is a (in general, non-proper) Lie automorphism of I(X, F). Finally, if F = Z(2), then phi is the composition of a bijective shift map and a Lie automorphism of I(X, F). Under certain restrictions on the characteristic of F we also obtain descriptions of the bijective linear maps which preserve tripotents and, more generally, k-potents of I(X, F) for k >= 3. (c) 2021 Elsevier Inc. All rights reserved.
NSTL
Elsevier