共查询到20条相似文献,搜索用时 31 毫秒
1.
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),
2.
Kazuki Cho 《Linear algebra and its applications》2009,431(8):1218-1222
Let φ be a positive linear functional on Mn(C) and f,g mutually conjugate in the sense of Young. In this note we show a necessary and sufficient condition for the inequality
3.
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
4.
Let (P,?,∧) be a locally finite meet semilattice. Let
5.
Let H be the real quaternion algebra and Hn×m denote the set of all n×m matrices over H. Let P∈Hn×n and Q∈Hm×m be involutions, i.e., P2=I,Q2=I. A matrix A∈Hn×m is said to be (P,Q)-symmetric if A=PAQ. This paper studies the system of linear real quaternion matrix equations
6.
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 ,
7.
Sungwon Cho 《Journal of Mathematical Analysis and Applications》2007,336(1):372-398
Partial regularity is proved for Lipschitzian critical points of polyconvex functionals provided ‖DuL∞‖ is small enough. In particular, the singular set for a Lipschitzian critical point has Hausdorff dimension strictly less than n when ‖DuL∞‖ is small enough. Model problems treated include
8.
Fernanda Botelho 《Linear algebra and its applications》2011,435(6):1344-1355
In this paper, we consider projections on minimal norm ideals of B(H) that are represented as the average of two surjective isometries. We describe projections of the form
9.
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
10.
Chong Li Shujie Li Zhaoli Liu Jianzhong Pan 《Journal of Differential Equations》2008,244(10):2498-2528
In this paper, we study the structure of the Fucík spectrum of −Δ, the set of points (b,a) in R2 for which the equation
11.
Measures of weak noncompactness are formulae that quantify different characterizations of weak compactness in Banach spaces: we deal here with De Blasi's measure ω and the measure of double limits γ inspired by Grothendieck's characterization of weak compactness. Moreover for bounded sets H of a Banach space E we consider the worst distance k(H) of the weak∗-closure in the bidual of H to E and the worst distance ck(H) of the sets of weak∗-cluster points in the bidual of sequences in H to E. We prove the inequalities
12.
It is known that for any nonzero complex n×n matrices X and Y the quotient of Frobenius norms
13.
We prove that if Ω⊆R2 is bounded and R2?Ω satisfies suitable structural assumptions (for example it has a countable number of connected components), then W1,2(Ω) is dense in W1,p(Ω) for every 1?p<2. The main application of this density result is the study of stability under boundary variations for nonlinear Neumann problems of the form
14.
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
15.
Juan-Miguel Gracia 《Linear algebra and its applications》2009,430(4):1196-1215
Given four complex matrices A,B,C and D, where A∈Cn×n and D∈Cm×m, and given a complex number z0: What is the (spectral norm) distance from D to the set of matrices X∈Cm×m such that z0 is a multiple eigenvalue of the matrix
16.
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:
17.
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
18.
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
19.
Let F denote a field and let V denote a vector space over F with finite positive dimension. We consider a pair of linear transformations A:V→V and A∗:V→V that satisfy the following conditions: (i) each of A,A∗ is diagonalizable; (ii) there exists an ordering of the eigenspaces of A such that A∗Vi⊆Vi-1+Vi+Vi+1 for 0?i?d, where V-1=0 and Vd+1=0; (iii) there exists an ordering of the eigenspaces of A∗ such that for 0?i?δ, where and ; (iv) there is no subspace W of V such that AW⊆W, A∗W⊆W, W≠0, W≠V. We call such a pair a tridiagonal pair on V. It is known that d=δ and for 0?i?d the dimensions of coincide. The pair A,A∗ is called sharp whenever . It is known that if F is algebraically closed then A,A∗ is sharp. In this paper we classify up to isomorphism the sharp tridiagonal pairs. As a corollary, we classify up to isomorphism the tridiagonal pairs over an algebraically closed field. We obtain these classifications by proving the μ-conjecture. 相似文献