共查询到20条相似文献,搜索用时 15 毫秒
1.
Wai Kiu Chan Byeong Moon Kim Myung-Hwan Kim Byeong-Kweon Oh 《The Ramanujan Journal》2008,17(1):145-153
Let N and M be quadratic ?-lattices, and K be a sublattice of N. A representation σ:K→M is said to be extensible to N if there exists a representation ρ:N→M such that ρ | K =σ. We prove in this paper a local–global principle for extensibility of representation, which is a generalization of the main theorems on representations by positive definite ?-lattices by Hsia, Kitaoka and Kneser (J. Reine Angew. Math. 301:132–141, 1978) and Jöchner and Kitaoka (J. Number Theory 48:88–101, 1994). Applications to almost n-universal lattices and systems of quadratic equations with linear conditions are discussed. 相似文献
2.
B. M. Kim 《Commentarii Mathematici Helvetici》2000,75(3):410-414
In this paper, we will prove there are infinitely many integers n such that n
2— 1 is square-free and admits universal octonary diagonal quadratic forms.
Received: November 2, 1998. 相似文献
3.
W. Duke 《Journal of Number Theory》2005,110(1):37-43
A result from 1988 on the square-free integers represented by a positive definite ternary quadratic form with integral coefficients is made uniform in the determinant of the form. 相似文献
4.
We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures. 相似文献
5.
We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures. 相似文献
6.
D. W. Lewis 《Linear and Multilinear Algebra》1997,42(4):349-363
A characterization of finite Hankei matrices is given and it is shown that such matrices arise naturally as matrix representations of scaled trace forms of field extensions and etale algebras. An algorithm is given for calculating the signature and the Hasse invariant of these scaled trace forms. 相似文献
7.
It is investigated the necessary and sufficient conditions for the generalized quadraticity of a linear combination of any two generalized quadratic matrices. The main result obtained is, in a sense, a generalization of the main results given in [Uç M, Özdemir H, Özban AY. On the quadraticity of linear combinations of quadratic matrices. Linear Multilinear Algebra. 2015;63:1125–1137.] which contains many of the results in the literature related to idempotency or involutivity of the linear combinations of idempotent and/or involutive matrices, to the generalized quadratic matrices. 相似文献
8.
9.
10.
Abraham Berman Christopher King Robert Shorten 《Linear and Multilinear Algebra》2013,61(10):1117-1123
In this article, a general notion of common diagonal Lyapunov matrix is formulated for a collection of n?×?n matrices A 1,?…?,?A s , and cones k 1,?…?,?k s in ? n . Necessary and sufficient conditions are derived for the existence of a common diagonal Lyapunov matrix in this setting. The conditions are similar to and extend the well-known criteria for the case s?=?1, k 1?=?? n . 相似文献
11.
12.
Ahmet Tekcan 《Applications of Mathematics》2007,52(5):407-415
In this paper we consider proper cycles of indefinite integral quadratic forms F = (a, b, c) with discriminant Δ. We prove that the proper cycles of F can be obtained using their consecutive right neighbors R
i(F) for i ⩾ 0. We also derive explicit relations in the cycle and proper cycle of F when the length l of the cycle of F is odd, using the transformations τ(F) = (−a, b, −c) and ϰ(F) = (−c, b, −a). 相似文献
13.
Tatjana von Rosen 《Linear and Multilinear Algebra》2013,61(5):595-606
In this article, we derive explicit expressions for the entries of the inverse of a patterned matrix that is a sum of Kronecker products. This matrix keeps the Kronecker structure under matrix inversion, and it is used, for example, in statistics, in particular in the linear mixed model analysis. The obtained results present new and extended existing algorithms for the inversion of the considered patterned matrices. We also obtain a closed-form inverse in terms of block matrices. 相似文献
14.
Mustapha Raïssouli 《Linear and Multilinear Algebra》2019,67(2):213-220
Let T and S be two self-adjoint positive invertible operators of a complex Hilbert space H. In this paper, we investigate some inequalities involving the quadratic forms of the weighted arithmetic and harmonic means of T and S. Application for operator entropies is also discussed. 相似文献
15.
We investigate the non-diagonal normal forms of a quadratic form on , in particular for n = 3. For this case it is shown that the set of normal forms is the closure of a 5-dimensional submanifold in the 6-dimensional
Grassmannian of 2-dimensional subspaces of .
Received: 27 June 2008 相似文献
16.
Liqun HU 《Frontiers of Mathematics in China》2015,10(5):1101
For the normalized Fourier coefficients of Maass cusp forms λ(n) and the normalized Fourier coefficients of holomorphic cusp forms a(n), we give the bound of ∑ m 1 2 + m 2 2 + m 3 2 ≤ x λ ( m 1 2 + m 2 2 + m 3 2 ) Λ ( m 1 2 + m 2 2 + m 3 2 ) and ∑ m 1 2 + m 2 2 + m 3 2 ≤ x a ( m 1 2 + m 2 2 + m 3 2 ) Λ ( m 1 2 + m 2 2 + m 3 2 ) . 相似文献
17.
We investigate a connection between isolated sets of diagonals of a matrix and simplicial faces of the polytope Ω n of doubly stochastic matrices. We also consider the minimum permanent on simplicial faces of Ω n . 相似文献
18.
We extend an interesting theorem of Yuan [12] for two quadratic forms to three matrices. Let C
1, C
2, C
3 be three symmetric matrices in ℜ
n×n
, if max{x
T
C
1
x,x
T
C
2
x,x
T
C
3
x}≥0 for all x∈ℜ
n
, it is proved that there exist t
i
≥0 (i=1,2,3) such that ∑
i=1
3
t
i
=1 and ∑
i=1
3
t
i
C
i
has at most one negative eigenvalue.
Received February 18, 1997 / Revised version received October 1, 1997? Published online June 11, 1999 相似文献
19.
主要讨论一阶量子广义Kac-Moody代数U_q(2α)的结构,其中a∈Z0.在此基础上,刻画了量子广义代数U_q(g)的另一种整形式. 相似文献
20.
Walter Feit 《Linear and Multilinear Algebra》2013,61(1-2):25-32
We give safety neighbourhoods for the necessary conditions in the change of the Jordan canonical form of a matrix under small perturbations. We also obtain the minimum distance from an n × n complex matrix which has less than k nonconstant invariant factors (2≤ k≤ n) to the set of matrices which have more or equal to k. When k= 2, we get in particular the distance from a nonderogatory matrix to the set of derogatory matrices. 相似文献