共查询到20条相似文献,搜索用时 15 毫秒
1.
LiPing Huang 《中国科学A辑(英文版)》2009,52(11):2404-2418
Let D be a division ring with an involution-,H2(D) be the set of 2 × 2 Hermitian matrices over D. Let ad(A,B) = rank(A-B) be the arithmetic distance between A,B ∈ H2(D) . In this paper,the fundamental theorem of the geometry of 2 × 2 Hermitian matrices over D(char(D) = 2) is proved:if :H2(D) → H2(D) is the adjacency preserving bijective map,then is of the form (X) = tP XσP +(0) ,where P ∈ GL2(D) ,σ is a quasi-automorphism of D. The quasi-automorphism of D is studied,and further results are obtained. 相似文献
2.
LetD be a division ring which possesses an involution a → α . Assume that
is a proper subfield ofD and is contained in the center ofD. It is pointed out that ifD is of characteristic not two, D is either a separable quadratic extension of F or a division ring of generalized quaternions
over F and that if D is of characteristic two,D is a separable quadratic extension ofF. Thus the trace map Tr:D → F, a → a + a is always surjective, which is formerly posed as an assumption in the fundamental theorem of n×n hermitian
matrices overD when n ≥ 3 and now can be deleted. WhenD is a field, the fundamental theorem of 2 × 2 hermitian matrices overD has already been proved. This paper proves the fundamental theorem of 2×2 hermitian matrices over any division ring of generalized
quaternions of characteristic not two
This research was completed during a visit to the Academy of Mathematics and System Sciences, Chinese Academy of Sciences. 相似文献
3.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2005,127(3):1969-1975
The lower bound
l1 (A) - ln (A) \geqslant 2||A12 ||\lambda _1 (A) - \lambda _n (A) \geqslant 2\parallel A_{12} \parallel 相似文献
4.
We consider one typical two-parameter family of quadratic systems of 2 × 2 conservation laws, and study the geometry of the
behaviour of the possible solutions of the Riemann problem near an umbilic point, following the geometric approach presented
by Isaacson, Marchesin, Palmeira, Plohr, in A global formalism for nonlinear waves in conservation laws, Commun. Math. Phys. (1992). The corresponding phase portraits for the rarefaction curves, shock curves and composite curves
are discussed.
Financial support from FCT and Calouste Gulbenkian Foundation. 相似文献
5.
6.
We give some upper bounds on the dimension of the kernel of the cup product map $H^{1}(X,\mathbb{C}) \otimes H^{1}(X,\mathbb{C}) \to H^{2}(X,\mathbb{C})
7.
Kh. D. Ikramov 《Mathematical Notes》2010,88(1-2):228-237
Canonical forms of 2 × 2 matrices with respect to unitary congruence transformations are described. This makes it possible to formulate simple criteria for checking whether the given matrices are unitarily congruent. 相似文献
8.
In this paper, we study the perturbation of spectra for 2 × 2 operator matrices such as M X = ( 0 B A X ) and M Z = ( Z B A C ) on the Hilbert space H ?? K and the sets $\bigcap\limits_{X \in \mathcal{B}(K,H)} {P_\sigma (M_X )} ,\bigcap\limits_{X \in \mathcal{B}(K,H)} {R_\sigma (M_X )} $ and $\bigcap\limits_{Z \in \mathcal{B}(H,K)} {\sigma (M_Z )} ,\bigcap\limits_{Z \in \mathcal{B}(H,K)} {P_\sigma (M_Z )} ,\bigcap\limits_{Z \in \mathcal{B}(H,K)} {R_\sigma (M_Z )} ,\bigcap\limits_{Z \in \mathcal{B}(H,K)} {C_\sigma (M_Z )} $ , where R(C) is a closed subspace, are characterized 相似文献
9.
A. Ya. Belyankov 《Computational Mathematics and Mathematical Physics》2008,48(2):190-194
Algorithms for computing the commutator AB ? BA of 2 × 2 matrices A and B are proposed that involve five multiplications. 相似文献
10.
When and are given, we denote by the operator acting on the infinite dimensional separable Hilbert space of the form . In this paper, we first give some necessary and sufficient conditions for to be a left invertible operator (an upper semi-Weyl, upper semi-Fredholm) operator for some , which extend the corresponding results in Cao et al. (2006) [4], Cao and Meng (2005) [5], Hwang and Lee (2001) [12] and Li and Du (2006) [15]. Then we present some counter-examples. 相似文献
11.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2005,129(2):3772-3786
Let an n × n Hermitian matrix A be presented in block 2 × 2 form as
, where A12 ≠ 0, and assume that the diagonal blocks A11 and A22 are positive definite. Under these assumptions, it is proved that the extreme eigenvalues of A satisfy the bounds
12.
The boundedness below of 2×2 upper triangular operator matrices 总被引:2,自引:0,他引:2
Wen
and
are given we denote byM
C
an operator acting on the Hilbert space
of the form
13.
14.
Mathematical Notes - Consider an operator which is defined in Banach or Hilbert space X = X 1 × X 2 by the matrix $L = left( {begin{array}{*{20}{c}}A&;amp;B C&;amp;D end{array}}... 相似文献
15.
16.
We give an interpretation and a natural proof of the lemma of Herglotz on 2 × 2 symmetric matrices from the point of view of 3-dimensional Lorentz geometry and 2-dimensional hyperbolic geometry. This interpretation leads naturally to an analogous result on 2 × 2 matrices with trace 0. 相似文献
17.
We consider a random process which is some version of the Brownian bridge in the space SL(2,R). Under simplifying assumptions we show that the increments of this process increase as t as in the case of the usual Brownian motion in the Euclidean space. The main results describe the limiting distribution for properly normed increments. 相似文献
18.
We study the injective comodules for the coordinate bialgebra of quantum 2 × 2 matrices at a root of unity. The related GL 2 and SL 2 theories are also specified. 相似文献
19.
20.
设D是带对合-的除环(体),H2(D))为D上2×2 Hermitian矩阵的集合.设ad(A,B)=rank(A—B)是A,B∈H2(D)之间的算术距离.本文证明了D(char(D)≠2)上2×2 Hermitian矩阵几何的基本定理:如果φ:H2(D)→H2(D)是保粘切的双射,则η(X)=t^-PXσP+φ(0),其中P∈GL2(D),σ是D的一个拟自同构.研究了D的拟自同构,并得到进一步的结果. 相似文献
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