共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, the nonlinear matrix equation X + A∗XqA = Q (q > 0) is investigated. Some necessary and sufficient conditions for existence of Hermitian positive definite solutions of the nonlinear matrix equations are derived. An effective iterative method to obtain the positive definite solution is presented. Some numerical results are given to illustrate the effectiveness of the iterative methods. 相似文献
2.
Yuan Gong Sun 《Journal of Mathematical Analysis and Applications》2003,279(2):651-658
Some new oscillation criteria are established for the matrix linear Hamiltonian system X′=A(t)X+B(t)Y, Y′=C(t)X−A∗(t)Y under the hypothesis: A(t), B(t)=B∗(t)>0, and C(t)=C∗(t) are n×n real continuous matrix functions on the interval [t0,∞), (−∞<t0). These results are sharper than some previous results even for self-adjoint second order matrix differential systems. 相似文献
3.
Based on the elegant properties of the Thompson metric, we prove that the general nonlinear matrix equation Xq-A∗F(X)A=Q(q>1) always has a unique positive definite solution. An iterative method is proposed to compute the unique positive definite solution. We show that the iterative method is more effective as q increases. A perturbation bound for the unique positive definite solution is derived in the end. 相似文献
4.
B.P. Duggal 《Linear algebra and its applications》2007,422(1):331-340
A Hilbert space operator A ∈ B(H) is said to be p-quasi-hyponormal for some 0 < p ? 1, A ∈ p − QH, if A∗(∣A∣2p − ∣A∗∣2p)A ? 0. If H is infinite dimensional, then operators A ∈ p − QH are not supercyclic. Restricting ourselves to those A ∈ p − QH for which A−1(0) ⊆ A∗-1(0), A ∈ p∗ − QH, a necessary and sufficient condition for the adjoint of a pure p∗ − QH operator to be supercyclic is proved. Operators in p∗ − QH satisfy Bishop’s property (β). Each A ∈ p∗ − QH has the finite ascent property and the quasi-nilpotent part H0(A − λI) of A equals (A − λI)-1(0) for all complex numbers λ; hence f(A) satisfies Weyl’s theorem, and f(A∗) satisfies a-Weyl’s theorem, for all non-constant functions f which are analytic on a neighborhood of σ(A). It is proved that a Putnam-Fuglede type commutativity theorem holds for operators in p∗ − QH. 相似文献
5.
In this paper we study the class of square matrices A such that AA† − A†A is nonsingular, where A† stands for the Moore-Penrose inverse of A. Among several characterizations we prove that for a matrix A of order n, the difference AA† − A†A is nonsingular if and only if R(A)⊕R(A∗)=Cn,1, where R(·) denotes the range space. Also we study matrices A such that R(A)⊥=R(A∗). 相似文献
6.
Jing Cai 《Applied mathematics and computation》2010,217(1):117-4466
Nonlinear matrix equation Xs + A∗X−tA = Q, where A, Q are n × n complex matrices with Q Hermitian positive definite, has widely applied background. In this paper, we consider the Hermitian positive definite solutions of this matrix equation with two cases: s ? 1, 0 < t ? 1 and 0 < s ? 1, t ? 1. We derive necessary conditions and sufficient conditions for the existence of Hermitian positive definite solutions for the matrix equation and obtain some properties of the solutions. We also propose iterative methods for obtaining the extremal Hermitian positive definite solution of the matrix equation. Finally, we give some numerical examples to show the efficiency of the proposed iterative methods. 相似文献
7.
Let b = b(A) be the Boolean rank of an n × n primitive Boolean matrix A and exp(A) be the exponent of A. Then exp(A) ? (b − 1)2 + 2, and the matrices for which equality occurs have been determined in [D.A. Gregory, S.J. Kirkland, N.J. Pullman, A bound on the exponent of a primitive matrix using Boolean rank, Linear Algebra Appl. 217 (1995) 101-116]. In this paper, we show that for each 3 ? b ? n − 1, there are n × n primitive Boolean matrices A with b(A) = b such that exp(A) = (b − 1)2 + 1, and we explicitly describe all such matrices. 相似文献
8.
Wen Zhang 《Linear algebra and its applications》2011,435(6):1326-1335
Let A and B be (not necessarily unital or closed) standard operator algebras on complex Banach spaces X and Y, respectively. For a bounded linear operator A on X, the peripheral spectrum σπ(A) of A is the set σπ(A)={z∈σ(A):|z|=maxω∈σ(A)|ω|}, where σ(A) denotes the spectrum of A. Assume that Φ:A→B is a map the range of which contains all operators of rank at most two. It is shown that the map Φ satisfies the condition that σπ(BAB)=σπ(Φ(B)Φ(A)Φ(B)) for all A,B∈A if and only if there exists a scalar λ∈C with λ3=1 and either there exists an invertible operator T∈B(X,Y) such that Φ(A)=λTAT-1 for every A∈A; or there exists an invertible operator T∈B(X∗,Y) such that Φ(A)=λTA∗T-1 for every A∈A. If X=H and Y=K are complex Hilbert spaces, the maps preserving the peripheral spectrum of the Jordan skew semi-triple product BA∗B are also characterized. Such maps are of the form A?UAU∗ or A?UAtU∗, where U∈B(H,K) is a unitary operator, At denotes the transpose of A in an arbitrary but fixed orthonormal basis of H. 相似文献
9.
We show that a maximal curve over Fq2 given by an equation A(X)=F(Y), where A(X)∈Fq2[X] is additive and separable and where F(Y)∈Fq2[Y] has degree m prime to the characteristic p, is such that all roots of A(X) belong to Fq2. In the particular case where F(Y)=Ym, we show that the degree m is a divisor of q+1. 相似文献
10.
Joe Masaro 《Linear algebra and its applications》2008,429(7):1639-1646
Suppose that Y = (Yi) is a normal random vector with mean Xb and covariance σ2In, where b is a p-dimensional vector (bj), X = (Xij) is an n × p matrix with Xij ∈ {−1, 1}; this corresponds to a factorial design with −1, 1 representing low or high level respectively, or corresponds to a weighing design with −1, 1 representing an object j with weight bj placed on the left and right of a chemical balance respectively. E-optimal designs Z are chosen that are robust in the sense that they remain E-optimal when the covariance of Yi, Yi′ is ρ > 0 for i ≠ i′. Within a smaller class of designs similar results are obtained with respect to a general class of optimality criteria which include the A- and D-criteria. 相似文献
11.
Ameur Seddik 《Linear algebra and its applications》2007,424(1):177-183
Let A be a standard operator algebra acting on a (real or complex) normed space E. For two n-tuples A = (A1, … , An) and B = (B1, … , Bn) of elements in A, we define the elementary operator RA,B on A by the relation for all X in A. For a single operator A∈A, we define the two particular elementary operators LA and RA on A by LA(X) = AX and RA(X) = XA, for every X in A. We denote by d(RA,B) the supremum of the norm of RA,B(X) over all unit rank one operators on E. In this note, we shall characterize: (i) the supremun d(RA,B), (ii) the relation , (iii) the relation d(LA − RB) = ∥A∥ + ∥B∥, (iv) the relation d(LARB − LBRA) = 2∥A∥ + ∥B∥. Moreover, we shall show the lower estimate d(LA − RB) ? max{supλ∈V(B)∥A − λI∥, supλ∈V(A)∥B − λI∥} (where V(X) is the algebraic numerical range of X in A). 相似文献
12.
13.
Elói Medina Galego 《Journal of Mathematical Analysis and Applications》2008,338(1):653-661
We first introduce the notion of (p,q,r)-complemented subspaces in Banach spaces, where p,q,r∈N. Then, given a couple of triples {(p,q,r),(s,t,u)} in N and putting Λ=(q+r−p)(t+u−s)−ru, we prove partially the following conjecture: For every pair of Banach spaces X and Y such that X is (p,q,r)-complemented in Y and Y is (s,t,u)-complemented in X, we have that X is isomorphic Y if and only if one of the following conditions holds:
- (a)
- Λ≠0, Λ divides p−q and s−t, p=1 or q=1 or s=1 or t=1.
- (b)
- p=q=s=t=1 and gcd(r,u)=1.
14.
Chun-Gil Park 《Journal of Mathematical Analysis and Applications》2005,307(2):753-762
It is shown that every almost linear bijection of a unital C∗-algebra A onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all unitaries u∈A, all y∈A, and n=0,1,2,…, and that almost linear continuous bijection of a unital C∗-algebra A of real rank zero onto a unital C∗-algebra B is a C∗-algebra isomorphism when h(n2uy)=h(n2u)h(y) for all , all y∈A, and n=0,1,2,…. Assume that X and Y are left normed modules over a unital C∗-algebra A. It is shown that every surjective isometry , satisfying T(0)=0 and T(ux)=uT(x) for all x∈X and all unitaries u∈A, is an A-linear isomorphism. This is applied to investigate C∗-algebra isomorphisms between unital C∗-algebras. 相似文献
15.
Timur Oikhberg 《Journal of Functional Analysis》2007,246(2):242-280
Suppose (B,β) is an operator ideal, and A is a linear space of operators between Banach spaces X and Y. Modifying the classical notion of hyperreflexivity, we say that A is called B-hyperreflexive if there exists a constant C such that, for any T∈B(X,Y) with α=supβ(qTi)<∞ (the supremum runs over all isometric embeddings i into X, and all quotient maps of Y, satisfying qAi=0), there exists a∈A, for which β(T−a)?Cα. In this paper, we give examples of B-hyperreflexive spaces, as well as of spaces failing this property. In the last section, we apply SE-hyperreflexivity of operator algebras (SE is a regular symmetrically normed operator ideal) to constructing operator spaces with prescribed families of completely bounded maps. 相似文献
16.
Martine C.B. Reurings 《Linear algebra and its applications》2006,418(1):292-311
In this paper we will give necessary and sufficient conditions under which a map is a contraction on a certain subset of a normed linear space. These conditions are already well known for maps on intervals in R. Using the conditions and Banach’s fixed point theorem we can prove a fixed point theorem for operators on a normed linear space. The fixed point theorem will be applied to the matrix equation X = In + A∗f(X)A, where f is a map on the set of positive definite matrices induced by a real valued map on (0, ∞). This will give conditions on A and f under which the equation has a unique solution in a certain set. We will consider two examples of f in detail. In one example the application of the fixed point theorem is the first step in proving that the equation has a unique positive definite solution under the conditions on A. 相似文献
17.
Qi-Ru Wang 《Journal of Mathematical Analysis and Applications》2004,295(1):40-54
By employing a generalized Riccati technique and an integral averaging technique, new oscillation criteria are established for the linear matrix Hamiltonian system U′=A(x)U+B(x)V, V′=C(x)U−A∗(x)V under the assumption that all A(x), B(x)=B∗(x)>0, and C(x)=C∗(x) are n×n matrices of real-valued continuous functions on the interval I=[x0,∞) (−∞<x0). These criteria extend, improve, and unify a number of existing results and also handle cases not covered by known criteria. Several interesting examples that illustrate the importance of our results are included. 相似文献
18.
Let V denote a vector space with finite positive dimension. We consider a pair of linear transformations A : V → V and A∗ : V → V that satisfy (i) and (ii) below:
- (i)
- There exists a basis for V with respect to which the matrix representing A is irreducible tridiagonal and the matrix representing A∗ is diagonal.
- (ii)
- There exists a basis for V with respect to which the matrix representing A∗ is irreducible tridiagonal and the matrix representing A is diagonal.
19.
20.
Maria Adam 《Applied mathematics and computation》2011,217(9):4699-4709
For an n × n normal matrix A, whose numerical range NR[A] is a k-polygon (k ? n), an n × (k − 1) isometry matrix P is constructed by a unit vector υ∈Cn, and NR[P∗AP] is inscribed to NR[A]. In this paper, using the notations of NR[P∗AP] and some properties from projective geometry, an n × n diagonal matrix B and an n × (k − 2) isometry matrix Q are proposed such that NR[P∗AP] and NR[Q∗BQ] have as common support lines the edges of the k-polygon and share the same boundary points with the polygon. It is proved that the boundary of NR[P∗AP] is a differentiable curve and the boundary of the numerical range of a 3 × 3 matrix P∗AP is an ellipse, when the polygon is a quadrilateral. 相似文献