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1.
关于Hadamard不等式的再改进 总被引:4,自引:0,他引:4
本文提出并改进了文[1]中所给出的几个关于可除环上矩阵行列式的不等式,利用这些不等式我们给出了可除环上任意非奇异矩阵的经典Hadamard不等式的一个再改进. 定义1 设A=(a_(ij))_(n×n)是四元数除环Ω上的矩阵,A=(a_(ij))_(n×n)是A的共轭矩阵,如果A=A,则称A为自共轭矩阵,如果A的各阶主子式均为正实数,则称A为正定自共轭矩阵(文[2]定理4). 相似文献
2.
Hadamard定理在四元数除环上的改进 总被引:5,自引:0,他引:5
<正> 推广到实四元数除环Q上的可中心化非奇异阵A=(a_(ij))_(n×n),而det A是按照谢邦杰意义下的行列式.本文将改进(1)式.首先,将按照Dieudonne意义下的行列式作改进.其次,附带证明了这个改进的不等式对谢邦杰意义下的行列式仍然成立,因而也就改进了谢邦杰的推广定理. 相似文献
3.
四元数自共轭矩阵与行列式的几个定理 总被引:2,自引:0,他引:2
本文继续使用文献[1],[2],[3],[4],[5]的符号和术语。对四元数体Q上的自共轭矩阵与行列式进行讨论得到几个重要定理。为此,先作几点说明。 2.设A为四元数体Q上的一个n阶矩阵,若A=(即,A=a_(ij),a_(ij)∈Q。恒有a_(ij)=a_(ji))。则说A是四元数体Q上的一个自共轭矩阵。自共轭四元矩阵A的行列式记为‖A‖。 相似文献
4.
本文证明了下列结果:(i)四元数矩阵A可写成两个自共轭四元数矩阵的乘积A相似于实矩阵A Hermite相似于A~*.(ii)A可写成一个半正定自共轭四元数矩阵与一个自共轭四元数矩阵的乘积A相似于实对角矩阵或者A~diag(D,I_r(×)J_2(O)),其中D是一个实对角矩阵.本文还给出了体上实矩阵AB与BA相似的一个充要条件. 相似文献
5.
预条件同时置换(PSD)迭代法的收敛性分析 总被引:4,自引:0,他引:4
1引言求解线性方程组Ax=6,(1.1)其中A∈R~(n×n)非奇异阵且对角元非零,x,b∈R~n,x未知,b已知.不失一般性,我们假设A=I-L-U,(1.2)其中L,U分别为A的严格下和上三角矩阵,相应的Jacobi迭代矩阵为B=L U.(1.3)若Q是非奇异阵且Q~(-1)易计算,于是(1.1)可以变成 相似文献
6.
四元数体上自共轭阵的中心化基本定理及其应用 总被引:5,自引:0,他引:5
如所周知,“复数域上 Hermite 阵酉相似于对角阵”这一基本结论已被推广到(实)四元数体 Q 上,即 Q 上 n 阶自共轭阵 A(A′=A)恒可中心化,也即存在 Q 上广义酉阵 U,((?)=U~(-1)),使其中λ_1,λ_2。…,n 是 Q 的中心(实数域 R)的元素。然而,(1)式却无助于特征值λ_1,λ_2,…,λ_n 的具体求法,也无助于 A 的按谢邦杰意义下的行列式的求法,本化将深化自共 相似文献
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9.
<正> §1.引言以 F_q 表 q 个元素的有限域,q 是一个素数的冪.考察 F_q 上所有 n 数组(x_1,x_2,…,x_n),x_i∈F_q,i=1,2,…,n,所组成的 n 维向量空间 V_n(F_q).V_n(F_q)的任—m 维子空间 P(1≤m≤n)都可以用一个秩为 m 的 m×n 矩阵来代表,只要这个矩阵的 m 个行向量组成 P 的一组基.我们把代表这个子空间 P 的矩阵仍记作 P.自然两个秩为 m 的m×n 矩阵 P 和 Q 代表同一子空间,当且仅当有 m×m 非奇异矩阵 A 存在使得 P=AQ.以下设 n=2ν是偶数,并考察 F_q 上的2ν×2ν的非奇异交错矩阵 相似文献
10.
1引 言设Cn×n为n×n复矩阵的集合,对A∈Cn×n,满足rank(Ak+1 )=rank( Ak)的最小非负整数k称为A的指标,记为Ind(A)=κ,则存在唯一矩阵AD∈Cn×n,满足下列矩阵方程组[1]:Ak=Ak+1AD AD=ADAAD AAD=ADAAD称为A的Drazin逆.若Ind(A)=1,则AD称为A的群逆,记为A#.显然Ind(A)=0当且仅当A非奇异,此时AD =A-1. 相似文献
11.
Let A, B be rings and P a radical property. Call B an A-Algebra if B is an A-bimodule such that (ba)b1 = b(ab1), (bb1)a = b(b1a), a(bb1) = (ab)b1 for any a ∈ A and any b,b1 ∈ B. A ring R, written as R = A ? B, is called a quasi-direct sum of (A, B) if A is a subring of R, B is an ideal of R and R is a direct sum of A and B as additive groups. The following results are obtained: 1. A quasi-direct sum of (A, B) is uniquely determined by an A-Algebra B (up to isomorphism); 2. The P-radical of the Algebra B is the same as the P-radical of the ring B; 3. P(A ? B) = P(A) +(B) if and only if P(A)B + BP(A) ? P(B); 4. If B has an identity e then P(A ? B) = P(A)(1?e) + P(B); 5. If P(Z) = 0 for the integer ring Z, then P(Mn(R)) = Mn(P(R)) holds for all rings R if and only if the above equality holds for all unitary rings R. In addition, some relationships of radicals between rings (or algebras over a field, semigroup algebras, etc.) and their corresponding identity extensions are discussed. 相似文献
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Dieter Kratsch 《Discrete Mathematics》2009,309(6):1724-1729
A graph H has the property MT, if for all graphs G, G is H-free if and only if every minimal (chordal) triangulation of G is H-free. We show that a graph H satisfies property MT if and only if H is edgeless, H is connected and is an induced subgraph of P5, or H has two connected components and is an induced subgraph of 2P3.This completes the results of Parra and Scheffler, who have shown that MT holds for H=Pk, the path on k vertices, if and only if k?5 [A. Parra, P. Scheffler, Characterizations and algorithmic applications of chordal graph embeddings, Discrete Applied Mathematics 79 (1997) 171-188], and of Meister, who proved that MT holds for ?P2, ? copies of a P2, if and only if ??2 [D. Meister, A complete characterisation of minimal triangulations of 2K2-free graphs, Discrete Mathematics 306 (2006) 3327-3333]. 相似文献
14.
Let A, B be associative rings with identity, and (S, ≤) a strictly totally ordered commutative monoid which is also artinian. For any bimodule AMB , we construct a bimodule A[[S]]M[S]B[[S]] and prove that AMB defines a quasi-duality if and only if the bimodule A[[S]]M[S]B[[S]] defines a quasi-duality. As a corollary, it is shown that if a ring A has a quasi-duality then the ring A[[S]] of generalized power series over A has a quasi-duality. 相似文献
15.
William H. Rowan 《Applied Categorical Structures》1998,6(1):63-86
We present two related categorical constructions. Given a category C, we construct a category C[d], the category of directed systems in C. C embeds into C[d], and if C has enough colimits, then C is monadic over C[d]. Also, if E,M is a factorization structure for C, then C[d] has a related factorization structure Ed Md such that if E consists entirely of monic arrows, then so does Ed and the Ed-quotient poset of an object A is naturally the poset of directed downsets of the E-quotient poset of A. Similarly, if M consists entirely of monicarrows, then so does Md and the Md-subobject poset of an object A is naturally the poset of directed downsets of the M-subobject poset. C[d] has completeness and cocompleteness properties at least as good as those of C, and it is abelian if C is. Dualization gives the other construction: a category C[i], the category of inverse systems in C, into which C also embeds and which satisfies similar properties, except that directed downsets in the E-quotient and M-subobject posets are replaced by directed upsets. 相似文献
16.
Jo Ann W. Staples 《Journal of Graph Theory》1979,3(2):197-204
A set of points in a graph is independent if no two points in the set are adjacent. A graph is well covered if every maximal independent set is a maximum independent set or, equivalently, if every independent set is contained in a maximum independent set. The well-covered graphs are classified by the Wn property: For a positive integer n, a graph G belongs to class Wn if ≥ n and any n disjoint independent sets are contained in n disjoint maximum independent sets. Constructions are presented that show how to build infinite families of Wn graphs containing arbitrarily large independent sets. A characterization of Wn graphs in terms of well-covered subgraphs is given, as well as bounds for the size of a maximum independent set and the minimum and maximum degrees of points in Wn graphs. 相似文献
17.
A graph is said to be super-connected if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected
if the deletion of each minimum vertex cut creates exactly two components, one of which is an isolated vertex. In this note,
we proved that a vertex transitive bipartite graph is not super-connected if and only if it is isomorphic to the lexicographic
product of a cycle Cn(n ≥ 6) by a null graph Nm. We also characterized non-hyper-connected vertex transitive bipartite graphs. 相似文献
18.
A graph G is a k-sphere graph if there are k-dimensional real vectors v
1,…,v
n
such that ij∈E(G) if and only if the distance between v
i
and v
j
is at most 1. A graph G is a k-dot product graph if there are k-dimensional real vectors v
1,…,v
n
such that ij∈E(G) if and only if the dot product of v
i
and v
j
is at least 1. 相似文献
19.
《Topology and its Applications》1986,23(1):65-73
It is well known that ℵ1 is a precaliber of Cp(X) for every Tychonoff space X. We prove under GCH that a compact space X is metrizable if and only if ℵ1 and ℵ2 are calibers of Cp(X). We show also that if X is a compact space then ℵ1 is a caliber of Cp(X) if and only if its diagonal Δ ⊂ X2 is small in the sense of Husek [9]. A similar method is used to establish that if X is an extremally disconnected compact space then Cp(X) admits a continuous injection into Σ1 (τ) (for some τ) if and only if the space X is separable. 相似文献
20.
A Lie subalgebraLof
(V) is said to befinitaryif it consists of elements of finite rank. We show that if Char
= 0, if dim
Vis infinite, and ifLacts irreducibly onV, then the derived algebra ofLis simple. 相似文献