偶特征正交空间上非奇异子空间的Critical问题

利用偶特征有限正交空间的性质及计数定理在偶特征有限正交空间上研究了非奇异子空间的critical问题,得到了相应的计数公式和critical指数.     

一类二元叠加码的构作及其d界

首先介绍了一种具有参数d,r的二元叠加(d,n,r)-码及偶特征正交空间上子空间的一些包含性质,然后利用这些性质及相关知识构作了二元叠加(d,n,r)-码并给出了其参数d的界.     

线性子空间关系运算的Pluecker坐标表示

本讨论了线性子空间Pluecker的线性表示,给出了Pluecker关系式的矩阵形式,并由之导出了子空间关联关系、零化子空间、和子空间与交子空间Pluecker坐标的矩阵表达式。     

n维欧氏空间的镜面反射

n维欧氏空间V的镜面反射是正交变换,镜面反射的逆变换仍为镜面反射;V上的正交变换同时为镜面反射的充要条件是它以1为特征值且其属于1的特征子空间是(n-1)维的;镜面反射在V的任一标准正交基下的矩阵具有形式En-2uu′,反之,若正交变换在V的某一标准正交基下的矩阵具有该形式,则它为镜面反射,其中u为列向量;V的任一正交变换可表为镜面反射的乘积.     

线性子空间关系运算的Pl cker坐标表示

本文讨论了线性子空间Pl cker的线性表示,给出了Pl cker关系式的矩阵形式,并由之导出了子空间关联关系、零化子空间、和子空间与交子空间Pl cker坐标的矩阵表达式.     

希尔伯特空间上的李雅普诺夫定理

我们用■(C)记n维欧氏空间 C~n 上的 n×n 阶矩阵全体,其中自共轭矩阵全体记为■_n.关于矩阵的 Lyapunov 定理和 Stein 定理通常分别叙述成Lyapunov 定理.对矩阵 A∈■(C),存在一自共轭矩阵 x∈■_n,且 X>0(正定),使 AX XA~*>0的充要条件是 A 的特征值完全落在复平面的右半开平面内.这里 A~*表示 A 的转置共轭矩阵,而右半开平面是指不包含虚轴的右半平面.     

Orlicz序列空间的装球常数

本文得到赋Orlicz范数的Orlicz序列空间的装球常数△_M的确切表示式,包含了Rankin,Burlack,和Cleaver关于l_2,l_p(p>1)和I_M的工作,利用这个表示式又获得I_M自反性的一个几何特征。     

基于空间错误逻辑变量未知的对象识别状态与应该状态之间的转化

讨论了在错误逻辑变量中,论域、事物、特征、量值等参数为确定常量的条件下,讨论空间参数为变量且未知时,错误的识别状态转化为应该状态的方程及其求解。研究发现,当对象识别状态当前的空间包含于应该状态当前的空间时,可以采用错误矩阵一类5集合方程A∧X_(qg)?B_g构建错误矩阵集合方程求解;当对象应该状态当前的空间包含于识别状态当前的空间时,可以采用错误矩阵一类4集合方程A∨X_(qg)?B_g构建一元置换变换错误矩阵集合方程,求解识别状态和应该状态的转化。     

特征为2的有限正交空间上全奇异子空间的Critical问题

利用特征为2的有限正交空间的性质及计数定理在特征为2的有限正交空间上研究了全奇异子空间的Critical问题,得到了相应的计数公式和Critical指数.     

奇特征有限正交空间中非迷向子空间的Critical问题

利用奇特征正交空间的性质及计数定理在奇特征正交空间中研究了非迷向子空间的Critical问题,得到了相应的计数公式和Critical指数.     

Wavelet representations and Fock space on positive matrices

We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations is shown to have tractable finite-dimensional co-invariant doubly cyclic subspaces. Further, motivated by these representations, we introduce a general Fock-space Hilbert space construction which yields creation operators containing the Cuntz-Toeplitz isometries as a special case.     

Incidence modules for symplectic spaces in characteristic two

We study the permutation action of a finite symplectic group of characteristic 2 on the set of subspaces of its standard module which are either totally isotropic or else complementary to totally isotropic subspaces with respect to the alternating form. A general formula is obtained for the 2-rank of the incidence matrix for the inclusion of one-dimensional subspaces in the distinguished subspaces of a fixed dimension.     

A magic decomposition

A lively example to use in a first course in linear algebra to clarify vector space notions is the space of square matrices of fixed order with its subspaces of affine, coaffine, doubly affine, and magic squares. In this note, the projection theorem is illustrated by explicitly constructing the orthogonal projections (in closed forms) of any matrix U onto these subspaces. The results follow directly from a canonical decomposition of U.     

Schur Orthogonality Relations for the Finitary Infinite Symmetric Group

Let S f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S f , a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms.     

Schur Orthogonality Relations for the Finitary Infinite Symmetric Group

Let S f be the finitary infinite symmetric group. For a certain class of irreducible unitary representations of S f , a version of Schur orthogonality relations is proved. That is, we construct an invariant inner product on the matrix coefficient space of each representation and show that matrix coefficients for distinct representations are orthogonal with respect to these norms.     

A new concept for block operator matrices:the quadratic numerical range

In this paper a new concept for 2×2-block operator matrices – the quadratic numerical range – is studied. The main results are a spectral inclusion theorem, an estimate of the resolvent in terms of the quadratic numerical range, factorization theorems for the Schur complements, and a theorem about angular operator representations of spectral invariant subspaces which implies e.g. the existence of solutions of the corresponding Riccati equations and a block diagonalization. All results are new in the operator as well as in the matrix case.     

RICE CONDITION NUMBERS OF CERTAIN CHARACTERISTIC SUBSPACES

This paper proposes the Rice condition numbers for invariant subspace, singular sub-spaces of a matrix and deflating subspaces of a regular matrix pair. The first-order perturbation estimations for these subspaces are derived by applying perturbation expansions of orthogonal projection operators.     

Eigenvalues of products of unitary matrices and Lagrangian involutions

This paper introduces a submanifold of the moduli space of unitary representations of the fundamental group of a punctured sphere with fixed local monodromy. The submanifold is defined via products of involutions through Lagrangian subspaces. We show that the moduli space of Lagrangian representations is a Lagrangian submanifold of the moduli of unitary representations.