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1.
The inequalities su At su Am ≥ su Ap su Aq and At+ su Am≥ su Ap+ su Aq are studied and generalized. Here su A denotes the sum of elements of the square matrix A. 相似文献
2.
Fernando C. Silva 《Linear and Multilinear Algebra》1990,27(4):317-323
Let F be a field and let A and n × n matrices over F. We study some properties of A' + B' and A'B', when A' and B' run over the sets of the matrices similar to A and B, respectively. 相似文献
3.
Nonnegative matrices A whose Moore-Penrose generalized inverse A+ is nonnegative and has any one of the three equivalent properties (i) AA+ = A+A (ii) A+ = A, the group inverse, (iii) A+ = p(A), some polynomial in A with scalar coefficients, are characterized. This characterization generalizes known results on nonnegative matrices Awhose Moore-Penrose generalized inverse is equal to some power of A. 相似文献
4.
Barbu C. Kestenband 《Linear and Multilinear Algebra》1983,14(3):257-270
In a finite geometry of order q2 we define a (qmqr)-affine cap to be a set of cardinality qm which is a disjoint union ot qm affine subgeometrics AG(r,q). such that no three points are coliinear unless contained in the same AG(r,q).
Given a PG(n,q2), where n = 2t + 1 or 2t + 2, and an n + 1 by n + 1 Hermitian matrix H over Gh(q2) with minimal polynomial (x - λ)n + 1. we show that H induces a partition of the AG(n, q2) obtained by deleting a distinguished hyperplane from the PG, into (qn,ql + 1)-affine caps; these caps can be viewed as the "large points" of an AG (n,q) with a natural incidence relation. It is also shown that H induces another partition of AG(n,q2), into qn - l 1-caps, constituting the "large points" of an affine geometry AG(n + t + 1,q).
Also, the collineation C of PG(n, q2) given by xc = HTx induces collineations on the AG(n,q) and AG(n + t + 1,q). 相似文献
Given a PG(n,q2), where n = 2t + 1 or 2t + 2, and an n + 1 by n + 1 Hermitian matrix H over Gh(q2) with minimal polynomial (x - λ)n + 1. we show that H induces a partition of the AG(n, q2) obtained by deleting a distinguished hyperplane from the PG, into (qn,ql + 1)-affine caps; these caps can be viewed as the "large points" of an AG (n,q) with a natural incidence relation. It is also shown that H induces another partition of AG(n,q2), into qn - l 1-caps, constituting the "large points" of an affine geometry AG(n + t + 1,q).
Also, the collineation C of PG(n, q2) given by xc = HTx induces collineations on the AG(n,q) and AG(n + t + 1,q). 相似文献
5.
Na Na Luan 《数学学报(英文版)》2017,33(6):839-850
Let X~H= {X~H(t), t ∈ R_+} be a subfractional Brownian motion in R~d. We provide a sufficient condition for a self-similar Gaussian process to be strongly locally nondeterministic and show that X~H has the property of strong local nondeterminism. Applying this property and a stochastic integral representation of X~H, we establish Chung's law of the iterated logarithm for X~H. 相似文献
6.
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
7.
Let G be a group, and let α be a regular automorphism of order p2 of G, where p is a prime. If G is polycyclic-by-finite and the map ϕ : G →G defined by gϕ= [g,α] is surjective, then G is soluble. If G is polycyclic, then CG(αp) and G/[G,αp] are both nilpotent-by-finite. 相似文献
8.
取f为权为偶数k的全模群Γ = SL(2,Z)的Hecke特征型.定义Asymmf(n)为与f关联的m阶对称幂次L-函数的Dirichlet展开式的第n个正规化系数.本文中,我们给出了Σn0为一个正数. 相似文献
9.
Formulas for the doubly stochastic square roots of the idempotents are presented. Such square roots must necessarily satisfy per A2≤perA. 相似文献
10.
Lowell Abrams Donniell E. Fishking Silvia Valdes-Leon 《Linear and Multilinear Algebra》2000,47(2):129-136
Let B denote either of two varieties of order n Pascal matrix, i.e., one whose entries are the binomial coefficients. Let BR denote the reflection of B about its main antidiagonal. The matrix B is always invertible modulo n; our main result asserts that B-1 ≡ BR mod n if and only if n is prime. In the course of motivating this result we encounter and highlight some of the difficulties with the matrix exponential under modular arithmetic. We then use our main result to extend the "Fibonacci diagonal" property of Pascal matrices. 相似文献
11.
Let A be an n × n matrix with non-negative entries and no entry in (0, 1). We prove that there exist integers r, s with 0 r s 2n such that Ar As. We prove that 2n cannot be replaced with e√n log n. We also give an application to the theory of formal languages. 相似文献
12.
On infinite area for complex exponential function 总被引:1,自引:0,他引:1
Figen ilingir 《Chaos, solitons, and fractals》2004,22(5):1189-1198
This paper shows via a reduced family of examples, the relaxed Newton's method is applied to complex exponential function F(z)=zez and F(z)=zez2, the basin of roots has infinite area. In addition, we examined their computer pictures which are fractals for the relaxed Newton's basin. In fact, computer experiments F(z)=P(z)ez and F(z)=P(z)ez2, indicate this to hold for arbitrary non-constant polynomial P(z). 相似文献
13.
In this paper a technique is developed for the expansion of a rational matrix F(λ)=G(λ)L-1(λ)(orF(λ)=L-1(λ)G(λ)into block partial fractions when the denominator has multiple roots. The method consists in the construction of interpolating matrix polynomials and their properties. Moreover, the approach is extended when L(λ) has nonlinear divisors. 相似文献
14.
C. W. Norman 《Linear and Multilinear Algebra》1995,38(4):351-371
Let A, B denote the companion matrices of the polynomials xm,xn over a field F of prime order p and let λ,μ be non-zero elements of an extension field K of F. The Jordan form of the tensor product (λI + A)⊗(μI + B) of invertible Jordan matrices over K is determined via an equivalent study of the nilpotent tranformation S of m × n matrices X over F where(X)S = A TX + XB. Using module-theoretic concepts a Jordan basis for S is specified recursively in terms of the representations of m and n in the scale of p, and reduction formulae for the elementary divisors of S are established. 相似文献
15.
T. H. Pate 《Linear and Multilinear Algebra》1981,10(2):103-105
Let A be an nk × nk positive semi-definite symmetric matrix partitioned into blocks Aij each of which is an n × n matrix. In [2] Mine states a conjecture of Marcus that per(A) ≥ per(G) where G is the k × k matrix [per(Aij)]. In this paper we prove a weaker inequality namely that per(A) ≥ (k!)-1per(G). 相似文献
16.
Olga Taussky 《Linear and Multilinear Algebra》1973,1(1):5-8
The fact that every unitary matrix can be expressed in the form A-1A* (observed by C. R. Johnson) is interpreted as a "Hilbert Theorem 90" in rings with an involution. Several observations connected with this are included. 相似文献
17.
We give an example of a function p such that the Hardy-Littlewood maximal operator is not bounded on the generalized Lebesgue space Lp(x). 相似文献
18.
J. R. Wall 《Linear and Multilinear Algebra》1975,2(4):337-340
For a doubly stochastic matrix A, each of the equations x:aty= A and X Aty=t is shown to have doubly stochastic solutions X and Y if and only if A lies in a subgroup of the semigroup of all doubly stochastic matrices of a given order. All elements of this semigroup which are left regular, right regular, or intra-regular are identified. 相似文献
19.
V. Soltan 《Expositiones Mathematicae》2004,22(4):301-315
This survey covers various geometric results related to Choquet simplexes in the Euclidean space Ed; it describes the known properties of Choquet simplexes and marks still open problems. 相似文献
20.
Hsin Chu 《Linear and Multilinear Algebra》1984,15(3):285-312
Let G be a connected, complex, semi-simple Lie group Let g be an element in G. Let B be a Borel subgroup of G and g in B. Let m and n be the least positive integers such that the element gm lies on a one-parameter subgroup in G and the element gn lies on a one-parameter subgroup in B. We denote these integers by indG(g) and indB(g). In this note we prove the conjecture indG(g) = indB(g), if g is regular. 相似文献