共查询到20条相似文献,搜索用时 31 毫秒
1.
A min-max theorem for complex symmetric matrices 总被引:1,自引:0,他引:1
Jeffrey Danciger 《Linear algebra and its applications》2006,412(1):22-29
We optimize the form Re xtTx to obtain the singular values of a complex symmetric matrix T. We prove that for ,
2.
Fang Jia 《Differential Geometry and its Applications》2007,25(5):433-451
Let be a locally strongly convex hypersurface, given by the graph of a convex function xn+1=f(x1,…,xn) defined in a convex domain Ω⊂Rn. M is called a α-extremal hypersurface, if f is a solution of
3.
Preservers of spectral radius, numerical radius, or spectral norm of the sum on nonnegative matrices
Chi-Kwong Li 《Linear algebra and its applications》2009,430(7):1739-1398
Let be the set of entrywise nonnegative n×n matrices. Denote by r(A) the spectral radius (Perron root) of . Characterization is obtained for maps such that r(f(A)+f(B))=r(A+B) for all . In particular, it is shown that such a map has the form
4.
Let V be a vector space over a field or skew field F, and let U be its subspace. We study the canonical form problem for bilinear or sesquilinear forms
5.
We find lower bounds on the difference between the spectral radius λ1 and the average degree of an irregular graph G of order n and size e. In particular, we show that, if n ? 4, then
6.
The higher Randi? index Rt(G) of a simple graph G is defined as
7.
Let (P,?,∧) be a locally finite meet semilattice. Let
8.
Walks and the spectral radius of graphs 总被引:1,自引:0,他引:1
Vladimir Nikiforov 《Linear algebra and its applications》2006,418(1):257-268
Given a graph G, write μ(G) for the largest eigenvalue of its adjacency matrix, ω(G) for its clique number, and wk(G) for the number of its k-walks. We prove that the inequalities
9.
Let A be an n×n complex matrix and c=(c1,c2,…,cn) a real n-tuple. The c-numerical range of A is defined as the set
10.
Aljoša Peperko 《Linear algebra and its applications》2008,428(10):2312-2318
Let Ψ be a bounded set of n×n non-negative matrices. Recently, the max algebra version μ(Ψ) of the generalized spectral radius of Ψ was introduced. We show that
11.
M.I. Gil’ 《Linear algebra and its applications》2008,428(4):814-823
The paper deals with an entire matrix-valued function of a complex argument (an entire matrix pencil) f of order ρ(f)<∞. Identities for the following sums of the characteristic values of f are established:
12.
Aljoša Peperko 《Linear algebra and its applications》2011,435(4):902-907
Given a bounded set Ψ of n×n non-negative matrices, let ρ(Ψ) and μ(Ψ) denote the generalized spectral radius of Ψ and its max version, respectively. We show that
13.
Ming Cheng Tsai 《Linear algebra and its applications》2011,435(9):2296-2302
Let A be an n-by-n (n?2) matrix of the form
14.
Koenraad M.R. Audenaert 《Linear algebra and its applications》2006,413(1):155-176
Let A be a positive semidefinite matrix, block partitioned as
15.
This paper is concerned with solving linear system (In+BL?B2B1)x=b arising from the Green’s function calculation in the quantum Monte Carlo simulation of interacting electrons. The order of the system and integer L are adjustable. Also adjustable is the conditioning of the coefficient matrix to give rise an extreme ill-conditioned system. Two numerical methods based on the QR decomposition with column pivoting and the singular value decomposition, respectively, are studied in this paper. It is proved that the computed solution by each of the methods is weakly backward stable in the sense that the computed is close to the exact solution of a nearby linear system
16.
Marek Niezgoda 《Linear algebra and its applications》2010,433(1):136-640
Let a,b>0 and let Z∈Mn(R) such that Z lies into the operator ball of diameter [aI,bI]. Then for all positive definite A∈Mn(R),
17.
It is known that for any nonzero complex n×n matrices X and Y the quotient of Frobenius norms
18.
Ming Cheng Tsai 《Linear algebra and its applications》2011,435(2):243-2302
We show that if A is an n-by-n (n?3) matrix of the form
19.
Shaun Cooper 《Journal of Number Theory》2003,103(2):135-162
Let rk(n) denote the number of representations of an integer n as a sum of k squares. We prove that for odd primes p,
20.
Let X be a real finite-dimensional normed space with unit sphere SX and let L(X) be the space of linear operators from X into itself. It is proved that X is an inner product space if and only if for A,C∈L(X)