共查询到20条相似文献,搜索用时 437 毫秒
1.
G. T. Rublein 《Linear and Multilinear Algebra》1989,25(4):257-267
Given a pair of n×n matricesA and B, one may form a polynomial P(A,B,λ) which generalizes the characteristic polynomial of BP(B,λ). In particular, when A=I (identity), P(A, B,λ) = P(B,λ), the characteristic polynomial of B. C. Johnson has conjectured [1] (among other things) that when A and B are hermitian and A is positive definite, then P(A,B,λ) has real roots. The case n=2 can be done by hand. In this paper we verify the conjecture for n=3. 相似文献
2.
D. B. Hunter 《Linear and Multilinear Algebra》1986,20(1):17-26
A derivation for the kernel of the irreducible representation T(λ) of the general linear group GLn(C) is given. This is then applied to the problem of determining necessary and sufficient conditions under which T(λ)(A) = T(λ)(B), where A and B are linear transformations, not necessarily invertible. Finally, conditions are obtained under which normality of T(λ)(A) implies normality of A. 相似文献
3.
A theorem of the alternatives for the equation Ax + B|x| = b 总被引:4,自引:0,他引:4
Jiri Rohn 《Linear and Multilinear Algebra》2004,52(6):421-426
The following theorem is proved: given square matrices A, D of the same size, D nonnegative, then either the equation Ax + B|x| = b has a unique solution for each B with |B| ≤ D and for each b, or the equation Ax + B0|x| = 0 has a nontrivial solution for some matrix B0 of a very special form, |B0| ≤ D; the two alternatives exclude each other. Some consequences of this result are drawn. In particular, we define a λ to be an absolute eigenvalue of A if |Ax| = λ|x| for some x ≠ 0, and we prove that each square real matrix has an absolute eigenvalue. 相似文献
4.
King-wah Eric Chu 《Applied Mathematics Letters》1988,1(4):343-346
We sketch some recent results in the perturbation theory of the matrix eigenvalue problems Ax = λx and Ax = λBx for multiple eigenvalues. Two quite different approaches — generalizing the Bauer-Fike Theorem and differentiating the eigensystems — have been used. 相似文献
5.
M. Barraa 《Linear algebra and its applications》2002,350(1-3):289-292
Let E,F be two Banach spaces and let S be a symmetric norm ideal of L(E,F). For AL(F) and BL(E) the generalized derivation δS,A,B is the operator on S that sends X to AX−XB. A bounded linear operator is said to be convexoid if its (algebraic) numerical range coincides with the convex hull of its spectrum. We show that δS,A,B is convexoid if and only if A and B are convexoid. 相似文献
6.
7.
Morris Newman 《Linear and Multilinear Algebra》1975,3(1):95-98
The principal results are that if A is an integral matrix such that AAT is symplectic then A = CQ, where Q is a permutation matrix and C is symplectic; and that if A is a hermitian positive definite matrix which is symplectic, and B is the unique hermitian positive definite pth.root of A, where p is a positive integer, then B is also symplectic. 相似文献
8.
We prove that for λ ≥ 0, p ≥ 3, there exists an open ball B L2(0,1) such that the problem , subject to certain separated boundary conditions on (0,1), has a solution for f B. 相似文献
− (|u′|p−2 u′)′ − λ|u|p−2u = f, in (0,1)
9.
Hans Joachim Werner 《Linear and Multilinear Algebra》1994,37(4):273-278
A real m×n matrix A is said to be semipositive if there is a nonnegative vector λ such that Ax exists and is componentwise positive. A is said to be minimally semipositive if it is semipositive and no proper m×p submatrix of A is semipositive. Minimal semipositivity is characterized in this paper and is related to rectangular monotonicity and weak r-monotonicity. P-matrices and nonnegative matrices will also be considered. 相似文献
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12.
Huang Liping 《Linear and Multilinear Algebra》1998,45(2):99-107
Let Rbe a finite dimensional central simple algebra over a field FA be any n× n matrix over R. By using the method of matrix representation, this paper obtains the structure formula of the minimal polynomial qA(λ) of A over F. By using qA(λ), this paper discusses the structure of right (left) eigenvalues set of A, and obtains the necessary and sufficient condition that a matrix over a finite dimensional central division algebra is similar to a diagonal matrix. 相似文献
13.
Morris Newman 《Linear and Multilinear Algebra》1982,11(4):363-366
Let Rbe a principal ideal ringRn the ring of n× nmatrices over R, and dk(A) the kth determinantal divisor of Afor 1 ≤ k≤ n, where Ais any element of Rn, It is shown that if A,BεRn, det(A) det(B:) ≠ 0, then dk(AB) ≡ 0 mod dk(A) dk(B). If in addition (det(A), det(B)) = 1, then it is also shown that dk(AB) = dk(A) dk(B). This provides a new proof of the multiplicativity of the Smith normal form for matrices with relatively prime determinants. 相似文献
14.
C. S. Ballantine 《Linear and Multilinear Algebra》1975,3(1):19-23
Matrices A,B over an arbitrary field F, when given to be similar to each other, are shown to be involutorily similar (over F) to each other (i.e.B = CAC-1for some C = C-1over F) in the following cases: (1)B= aI - Afor some a ε F and (2) B = A-1. Result (2) for the cases where char F ≠ 2 is essentially a 1966 result of Wonenburger. 相似文献
15.
Takayuki Hibi 《Journal of Pure and Applied Algebra》1989,60(3):245-251
Let A = A0A1 be a commutative graded ring such that (i) A0 = k a field, (ii) A = k[A1] and (iii) dimk A1 < ∞. It is well known that the formal power series ∑∞n = 0 (dimkAn)λ n is of the form (h0 + h1λ + + hsλs)/(1 − λ)dimA with each hiε
. We are interested in the sequence (h0, h1,…,hs), called the h-vector of A, when A is a Cohen–Macaulay integral domain. In this paper, after summarizing fundamental results (Section 1), we study h-vectors of certain Gorenstein domains (Section 2) and find some examples of h-vectors arising from integrally closed level domains (Sections 3 and 4). 相似文献
16.
J. Arvesú R. Álvarez-Nodarse F. Marcellán K. Pan 《Journal of Computational and Applied Mathematics》1998,90(2):263-156
We obtain an explicit expression for the Sobolev-type orthogonal polynomials {Qn} associated with the inner product , where p(x) = (1 − x)(1 + x)β is the Jacobi weight function, ,β> − 1, A1,B1,A2,B20 and p, q P, the linear space of polynomials with real coefficients. The hypergeometric representation (6F5) and the second-order linear differential equation that such polynomials satisfy are also obtained. The asymptotic behaviour of such polynomials in [−1, 1] is studied. Furthermore, we obtain some estimates for the largest zero of Qn(x). Such a zero is located outside the interval [−1, 1]. We deduce his dependence of the masses. Finally, the WKB analysis for the distribution of zeros is presented. 相似文献
17.
Stephen L. Campbell 《Linear and Multilinear Algebra》1978,6(1):55-59
The existence of the limit as ε→0 exp[(A+B/ε)t] exp[-Bt/ε]is studied for n×n matrices A,B. Necessary and sufficient conditions on B that the limit exist for all A are given. 相似文献
18.
Many different fuzzy implication operators have been proposed; most of them fit into one of the two classes: implication operations that are based on an explicit representation of implication A → B in terms of &, , and ¬ (e.g., S-implications that are based on the formula B ¬ A), and R-implications that are based on an implicit representation of implication A → B as the weakest C for which C&B implies A. However, some fuzzy implication operations (such as ba) cannot be naturally represented in this form. To describe such operations, we propose a new (third) class of implication operations called A-implications whose relation to &, , and ¬ is described by (implicit) axioms. 相似文献
19.
Linear operators that preserve pairs of matrices which satisfy extreme rank properties 总被引:4,自引:0,他引:4
LeRoy B. Beasley Sang-Gu Lee Seok-Zun Song 《Linear algebra and its applications》2002,350(1-3):263-272
A pair of m×n matrices (A,B) is called rank-sum-maximal if rank(A+B)=rank(A)+rank(B), and rank-sum-minimal if rank(A+B)=|rank(A)−rank(B)|. We characterize the linear operators that preserve the set of rank-sum-minimal matrix pairs, and the linear operators that preserve the set of rank-sum-maximal matrix pairs over any field with at least min(m,n)+2 elements and of characteristic not 2. 相似文献
20.
Carlos Gamas 《Linear and Multilinear Algebra》2000,47(2):151-173
Let λ be an irreducible character of Sn corresponding to the partition (r,s) of n. Let A be a positive semidefinite Hermitian n × n matrix. Let dλ(A) and per(A) be the immanants corresponding to λ and to the trivial character of Sn, respectively. A proof of the inequality dλ(A)≤λ(id)per(A) is given. 相似文献