自由函子及其伴随函子

本文证明了由集合范畴到f-模范畴的自由函子的存在性，构造了自由函子的伴随函子。     

函子范畴上加性函子的一个表示

研究函子范畴ModC上加性函子的表示,把一个Abel群作成范畴ModC上的一个左C-模,构造出一个Hom函子和一个函子态射,证明了从函子范畴ModC到范畴Ab的任意变和为积的反变左正合可加函子都与某个Hom函子自然等价.所得结论在函子范畴上,推广了Watts定理.     

态射的广义逆与等化子

本文以态射偶的等化子为工具研究态射的广义逆，对于态射f，给出了g为f^-,f^D和f^ 的充要条件，并在矩阵范畴中建立了齐次线性方程组解与等化子的关系。     

同调函子的一个应用

本文利用同调函子给出了交换的 Noether环上单模的投射性与内射性是等价的一个简单证明 ,同时推广了文 [1]的一些结论     

广义Schur补的广义逆

对四分块矩阵A=A(︿) A(︿,︿′)A(︿′,︿) A(︿′)来说 ,如果 A和 A(︿)都是非奇异的 ,则A- 1 (︿′) =(A/︿) - 1 ,这里 A/ ︿=A(︿′) -A(︿′,︿) A(︿) - 1 A(︿,︿′)是 A(︿)在 A中的 Schur补 .王伯英教授指出上述等式 ,对半正定的 Hermitian矩阵而言 ,一般也是不能推广到 Moore-Penrose逆上去的 .在某些限制条件下 ,我们证明了广义逆的主子矩阵与广义 Schur补的关系是密切的 ,它使经典结果成为特例     

Banach空间中线性算子的齐性广义逆

本文首先在Banach空间内引进拟线性投影算子的概念,由此给出Banach空 间内线性算子的齐性广义逆的统一定义。齐性广义逆包含线性广义逆、单值度量广义 逆.本文证得齐性广义逆存在的充分必要条件.     

关于广义逆的注记

本文得到下列结果:命题1,在算子代数A 中充分必要条件(1,2)—A 存在的广义逆是(1)—A 存在的广义逆。命题2,让F 是一个域,4∈F~(mrn),(1.2)—A 的广义逆总是存在的.     

广义Schur补的广义逆

对四分块矩阵a=[A(α） A（α，α′）A（α′，α） A（α′）]来说，如果A和A（α）都是非奇异的，则A^-1(α′）=（A/α）^-1,这里A／α=A（α′）-A（α′，α）A（α）^-1A(α，α′）是A（α）在A中的Schur补。王伯英教授指出上述等式，对半正定的Hermitian矩阵而言，一般也是不能推广到Moore-Penrose逆上去的。在某些限制条件下，我们证明了广义逆的主子矩阵与广义Schur补的关系是密切的，它使经典结果成为特例。     

函子范畴的等价

本文建立了函子范畴等价的Ｍｏｒｉｔａ理论．考虑的主要问题是ｍｏｄＣ何时等价于ｍｏｄＣ′及这些等价条件．同时定义了函子范畴的双模和函子张量积，并刻画了等价函子．     

关于平移函子

设室 C∈V~(p-1)ρ,λ,μ∈(?)。令η∈X(T)满足 λ+pη∈X(T)_(+(?))当μ属于包含λ的片的闭包时,平移 T_(λ+pη)~(μ+pη)L(λ+pη)是已知的(参看[1]或[2])。今设λ,μ∈(?),Stnb_W_p(λ)={1,y}本文得到了平移公式 T_(λ+pη)~(μ+pη)L(λ+pη)。作为本文结果的一个应用,我们对于 G=SL_3的情形,给出了形式特征标 chT_(λ+pη)~(μ+pη)L(λ+pη)。     

Tambara Functors on Profinite Groups and Generalized Burnside Functors

The Tambara functor was defined by Tambara in the name of TNR-functor, to treat certain ring-valued Mackey functors on a finite group. Recently Brun revealed the importance of Tambara functors in the Witt–Burnside construction. In this article, we define the Tambara functor on the Mackey system of Bley and Boltje. Yoshida's generalized Burnside ring functor is the first example. Consequently, we can consider a Tambara functor on any profinite group. In relation with the Witt–Burnside construction, we can give a Tambara-functor structure on Elliott's functor V _M , which generalizes the completed Burnside ring functor of Dress and Siebeneicher.     

Generalized Inverses of Matrices over Rings

Let R be a ring, * be an involutory function of the set of all finite matrices over R. In this paper, necessary and sufficient conditions are given for a matrix to have a (1,3)-inverse, (1,4)-inverse, or Moore-P enrose inverse, relative to *. Some results about generalized inverses of matrices over division rings are generalized and improved.     

关于布尔矩阵的广义Moore-Penrose逆

讨论布尔矩阵的广义Moore-Penrose逆.给出了一些广义Moore-Penrose逆存在的充要条件以及广义Moore-Penrose逆的一些刻划.     

Strongly Involutory Functors

Let 𝒞 be an arbitrary category. We study strongly involutory functors on 𝒞, defined as involutory contravariant endofunctors of 𝒞 acting as identity on objects. Motivating examples can be constructed if we think at the transpose of a matrix, the adjoint of a linear continuous operator between two Hilbert spaces, and the inverse of a morphism in a groupoid. We show how a strongly involutory functor on a skeleton of 𝒞 extends to 𝒞, and we apply this to find all such functors for a groupoid. We describe and classify up to a natural equivalence all strongly involutory functors on the category of finite dimensional vector spaces over a field. Strongly involutory functors with a special property related to generalized inverses of morphisms are studied.     

加权广义逆矩阵的反序律

研究了在权数矩阵M,N可逆的条件下加权广义逆的反序律,给出了多种表达式.     

集值度量广义逆的存在性

设X,Y为Banach空间,T∈L(X,Y)为从X到Y的线性算子,D(T),N(T),R(T)分别为T的定义域,核空间与值域,使用算子T的自身性质,给出T具有集值度量广义逆T和R(T)D(T)的充分必要条件.     

广义逆矩阵特征性质的注记

本文运用线性算子方法进一步探讨了一般数域上矩阵广义逆的特征性质,同时也分别简化和修正了文献［1］中定理2.3.5和定理2.3.6给出的矩阵广义逆A-的结果.     

Least Squares Properties of Generalized Inverses

The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses.As a significant application of the Moore-Penrose inverse,the best approximation solution to linear matrix equations (i.e.both least squares and the minimal norm) is considered.Also,characterizations of least squares solution and solution of minimum norm are given.Basic properties of the Drazin-inverse solution and the outer-inverse so-lution are present.Motivated by recent research,important least square prop-erties of composite outer inverses are collected.     

Least Squares Properties of Generalized Inverses

The aim of this paper is to systematize solutions of some systems of linear equations in terms of generalized inverses.As a significant application of the Moore-Penrose inverse,the best approximation solution to linear matrix equations (i.e.both least squares and the minimal norm) is considered.Also,characterizations of least squares solution and solution of minimum norm are given.Basic properties of the Drazin-inverse solution and the outer-inverse so-lution are present.Motivated by recent research,important least square prop-erties of composite outer inverses are collected.     

广义逆理论中一个定理的拓广

给出了广义逆理论一个定理的推广,解决了体上相容矩阵方程AX=H解的最简表达式问题.