共查询到20条相似文献,搜索用时 609 毫秒
1.
Leroy B. Beasley 《Linear and Multilinear Algebra》1978,6(3):179-183
Let L be a linear transformation on the set of all n×n matrices over an algebraically closed field of characteristic 0. It is shown that if AB=BA implies L(A)L(B)=L(B)L(A) and if either L is nonsingular or the implication in the hypothesis can also be reversed, then L is a sum of a scalar multiple of a similarity transformation and a linear functional times the identity transformation. 相似文献
2.
W. Y. Tan 《Mathematical and Computer Modelling》1991,15(12):37-65
Extending my previous work [1–3], in this paper I proceed to develop a stochastic model for HIV epidemic in a homosexual population under general conditions. Through computer generated data, I assess various deterministic models as compared with the expected numbers of the stochastic models. It is shown that different mixing patterns have significant impacts on the HIV epidemic except possibly restricted mixing. Thus, in populations with preferred mixing (mixing proportion less than 1) and with proportional mixing, the numbers of S people, L people, I people and A people differ significantly from the corresponding expected numbers of the stochastic models. For the L people, I people and A people, the numbers of the deterministic models first appear to be smaller and later appear to be larger than the corresponding mean numbers of the stochastic models, indicating that while in the short run the deterministic models would underestimate the true numbers, in the long run the deterministic models would overestimate the true numbers. 相似文献
3.
Let Λ = (S/R, ) be the crossed product order in the crossed product algebra A = (L/K, ) with factor set , where L/K is a Galois extension of the local field K, and R (resp. S) the valuation ring of K (resp. L). In this paper the maximal R-orders in A containing Λ and the irreducible Λ-lattices are determined. 相似文献
4.
Let X be a Banach space over F(= R or C) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B_0(X) the set spanned by N(X). We give a structure result to the additive maps on FI + B_0(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI + B_0(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A~(-1)+ φ(T)I for all T ∈ FI + B_0(X) or Φ(T) = cAT*A~(-1)+ φ(T)I for all T ∈ FI + B_0(X), where c is a nonzero scalar,A is a τ-linear bijective transformation for some automorphism τ of F and φ is an additive functional.In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator. 相似文献
5.
Russell Merris 《Linear and Multilinear Algebra》1989,25(4):291-296
Let T be a tree on n vertices. The Laplacian matrix is L(T)=D(T)-A(T), where D(T) is the diagonal matrix of vertex degrees and A(T) is the adjacency matrix. A special case of the Matrix-Tree Theorem is that the adjugate of L(T) is the n-by-n matrix of l's. The (n-l)-square "edge version" of L(T)is K(T). The main result is a graph-theoretic interpretation of the entries of the adjugate of K(T). As an application, it is shown that the Wiener Index from chemistry is the trace of this adjugate. 相似文献
6.
Fernando C. Silva 《Linear and Multilinear Algebra》1988,24(1):51-58
Let F be a field and let A,B be n × n matrices over I. We study the rank of A' - B' when A and B run over the set of matrices similar to A and B, respectively. 相似文献
7.
Associated to any simplicial complex Δ on n vertices is a square-free monomial ideal IΔ in the polynomial ring A = k[x1, …, xn], and its quotient k[Δ] = A/IΔ known as the Stanley-Reisner ring. This note considers a simplicial complex Δ* which is in a sense a canonical Alexander dual to Δ, previously considered in [1, 5]. Using Alexander duality and a result of Hochster computing the Betti numbers dimk ToriA (k[Δ],k), it is shown (Proposition 1) that these Betti numbers are computable from the homology of links of faces in Δ*. As corollaries, we prove that IΔ has a linear resolution as A-module if and only if Δ* is Cohen-Macaulay over k, and show how to compute the Betti numbers dimk ToriA (k[Δ],k) in some cases where Δ* is wellbehaved (shellable, Cohen-Macaulay, or Buchsbaum). Some other applications of the notion of shellability are also discussed. 相似文献
8.
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
9.
Takeo Yamada 《Linear and Multilinear Algebra》1988,22(4):313-323
Given an n×(n+I) sign matrix (Ab). we are concerned with the condition that guarantees the solution to Ax=b be of a fixded sign pattern. It is shown that each factor of det (1) corresponds. in aone to one way to DM-component of the bipartite graph representation of A. This fact is used to supplement the proof of the graph-theoretic characterization of sign-solvability obtained by Bassett et al. [1] and subsequent authors. 相似文献
10.
Denote by W(A) the numerical range of a bounded linear operator A. For two operators A and B (which may act on different Hilbert spaces), we study the relation between the inclusion relation W(A)⊆W(B) and the condition that A can be dilated to an operator of the form B⊗I. We also investigate the possibilities of dilating an operator A to operators with simple structure under the assumption that W(A) is included in a special region. 相似文献
11.
Ky Fan 《Linear and Multilinear Algebra》1992,32(2):89-92
We prove some inequalities for matrices A such that A - I is either a positive definite Hermitian matrix or an M -matrix where I stands for the identity matrix. 相似文献
12.
A simple intersection sensitive algorithm for the hidden line elimination problem, was presented by Nurmi in 1985. This algorithm has O((n + I) logn) time and space complexities, where n is the number of edges in the input scene and I is the number of their intersections on the projection plane. We describe a method that reduces the space requirements of the algorithm to O(n) while retaining the time complexity of O((n+I) logn). Furthermore we show that the algorithm can be easily extended to handle the more general problem of hidden surface removal. 相似文献
13.
In this note we present closed form formulae for the intersection A ∧ B under the star order, for certain pairs of special matrices. In particular, it is shown that for two m×n partial isometries P and QP∧Q=P[I-(I-P*Q)†(I-P*Q)]. Some further possible representations for P∧Q are considered. 相似文献
14.
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
15.
Endre Cski Mikls Csrg Antnia Fldes Pl Rvsz 《Stochastic Processes and their Applications》1997,70(2):199-217
We study the asymptotic behaviour of the occupation time process ∫t0 IA(W1(L2(s)))ds, t 0, where W1 is a standard Wiener process and L2 is a Wiener local time process at zero that is independent from W1. We prove limit laws, as well as almost sure upper and lower class theorems. Possible extensions of the obtained results are also discussed. 相似文献
16.
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
17.
A survey of graph laplacians 总被引:5,自引:0,他引:5
Russell Merris 《Linear and Multilinear Algebra》1995,39(1):19-31
Let G be a graph on n vertices. Its Laplacian is the n-by-n matrix L(G)-D(G)-A(G), where D(G) is the diagonal matrix of vertex degrees and A(G) is the (0,1)-adjacency matrix of G. This article surveys recent results on graph Laplacians. 相似文献
18.
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
19.
Manohar P. Kamat 《Finite Elements in Analysis and Design》1987,3(4):277-284
In this paper, the problem of optimization of shallow frame structures, which involves coupling of axial and bending responses, is discussed. A shallow arch of given shape and given weight is optimized such that its limit point load is maximized. The crosssectional area, A(x), and the moment of inertia, I(x), of the arch obey the relationship I(x) = [A(x)]n, where N = 1, 2, 3 and is a specified constant. Analysis of the arch for its limit point calculation involves a geometric nonlinear analysis which is performed using a co-rotational formulation.
The optimization is carried out using a second-order projected Langragian algorithm, and the sensitivity derivatives of the critical load parameter with respect to the areas of the finite elements of the arch are calculated using implicit differentiation. Results are presented for an arch of a specified rise to span under two different loadings, and the limitations of the approach for the intermediate rise arches are addressed. 相似文献
20.
David London 《Linear and Multilinear Algebra》1990,26(1):107-117
A necessary and sufficient condition for a matrix to be stochastically similar to a matrix with equal diagonal elements is obtained Aand B are called Stochastically similar if B=SAS- 1 where S is quasi-stochastic i.e., all row sums of .S are I. An inverse elementary divisor problem for quasi-stochastic matrices is also considered. 相似文献