保域上立方幂等矩阵的线性映射

设F是一个特征不为2及3的域，M．(F)记F上n阶全矩阵代数．本文在n≤m时得到了从M．(F)到Mm(F)的保立方幂等矩阵的线性映射的形式．作为应用又确定了保群逆线性映射形式．     

关于2×2矩阵代数保立方幂等的单射

刻画了2×2全矩阵代数保立方幂等映射,利用保立方幂等映射象与原象矩阵对应元素相等这个特点计算出相应的结果,得出特征不等于2,3,5域上2×2全矩阵代数保立方幂等单射的一个具体的刻画.     

关于2×2矩阵代数保立方幂等的单射

刻画了2×2全矩阵代数保立方幂等映射,利用保立方幂等映射象与原象矩阵对应元素相等这个特点计算出相应的结果,得出特征不等于2,3,5域上2×2全矩阵代数保立方幂等单射的一个具体的刻画.     

幂保持加法映射

本文得到了域上n×n矩阵代数的幂保持加法映射的刻画,同时刻画了对称矩阵的幂保持加法映射.     

关于幂等矩阵秩的一个等式

目的:将复数域上幂等矩阵秩的一个等式推广到除环上.方法:采用广义逆矩阵的理论.结果:得到了除环上的类似等式.结论:复幂等矩阵的某些等式是可以推广到除环上的,并且可以进行必要的改进.     

幂等阵和幂零阵的伴随阵的若干性质

本文利用极限过程的方法,证明了幂等阵和幂零阵的伴随矩阵分别是幂等阵和幂零阵．所得到的结论比［１］丰富得多．     

关于三角矩阵代数的幂保持加法算子

在最近几十年许多研究者一直研究线性保持问题和加法保持问题。假设k≥2是一个固定的正整数,F是一个域，其特征数大于k或为0．令Tn(F)是F上上三角矩阵代数．本文刻画了Tn(F)的幂保持加法算子．     

幂等右侧Quantale上的幂零矩阵

讨论幂等右侧Quantale上的幂零矩阵的若干性质，给出了幂等右侧Quantale上的矩阵为幂零矩阵的充要条件，得到了幂零矩阵的幂零指数的刻画定理。     

保特征2的域上幂等矩阵的线性算子

设Ｆ是特征２的域．本文确定Ｆ上ｎ×ｎ矩阵保幂等性的可逆的线性算子的半群Ｈ（Ｆ）的结构，同时回答了文献［１］提出的两个未解决的问题．     

反幂等阵线性组合的反幂等性

讨论了反幂等阵线性组合的幂等性,指出可对角化矩阵可表示为反幂等阵的线性组合,并由此得到了由非奇异矩阵构造两两正交且可交换的反幂等阵的一种方法.     

Additive Maps Preserving Moore-Penrose Inverses of Matrices on Symmetric Matrix Spaces

Suppose F is a field of characteristic not 2. Let M_nF and S_nF be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from S_nF to S_nF (respectively, M_nF) preserving Moore-Penrose inverses of matrices are characterized. We first characterize all additive Moore-Penrose inverse preserving maps from S_nF to M_nF, and thereby, all additive Moore-Penrose inverse preserving maps from S_nF to itself are characterized by restricting the range of these additive maps into the symmetric matrix space.     

保持交换环上两类矩阵运算的映射

主要针对交换环上两类矩阵的保持问题进行展开:(1)刻画了交换环上全矩阵空间和上三角形矩阵空间的保持反对合矩阵映射的形式.(2)研究了交换环上n阶上三角形矩阵空间的保持伴随矩阵映射的形式.     

Three linear preservers on infinite triangular matrices

We consider three linear preserver problems on the algebra of infinite triangular matrices over fields. We characterize the maps preserving invertible and noninvertible matrices, the surjective maps preserving inverses and the surjective maps preserving rank permutability.     

Continuous maps on triangular matrices that preserve commutativity

We investigate continuous injective maps defined on the space of upper triangular matrices over a field F that preserve commutativity of matrices in both directions. We show that every such map is a composition of either an inner automorphism and a locally polynomial map or the two latter and one more automorphism of upper triangular matrices.     

Additive Maps Preserving Moore–Penrose Inverses of Matrices on Symmetric Matrix Spaces

Suppose F is a field of characteristic not 2. Let M_n F and S_n F be the n × n full matrix space and symmetric matrix space over F, respectively. All additive maps from S_n F to S_n F (respectively, M_n F) preserving Moore–Penrose inverses of matrices are characterized. We first characterize all additive Moore–Penrose inverse preserving maps from S_n F to M_n F, and thereby, all additive Moore–Penrose inverse preserving maps from S_n F to itself are characterized by restricting the range of these additive maps into the symmetric matrix space.     

域上两类矩阵保逆的诱导映射

令F是一个域,S_n(F)是F上所有n×n上对称矩阵的集合.用T_n(F)记F上所有n阶上三角阵的集合.首先分别给出诱导映射和保逆性的定义.然后改进了关于复对称阵保逆的主要相关结果及其证明,得到了S_n(F)保逆诱导映射的一般形式,最后借助于类序列技术和初等方法刻画了T_n(F)保逆诱导映射.它推广和改进了带有附加条件(f_(ij)(x)=0x=0)的相关结果.     

矩阵代数上保持与正矩阵的相似性的可加满射

用M_n表示n×n复矩阵代数(n≥2),给出M_n上双边保与正矩阵的相似性的可加满射的完全刻画和分类.     

Linear Maps Preserving Idempotency of Products of Matrices on Upper Triangular Matrix Algebras

Let Tn be the algebra of all n × n complex upper triangular matrices. We give the concrete forms of linear injective maps on Tn which preserve the nonzero idempotency of either products of two matrices or triple Jordan products of two matrices.     

从对称矩阵代数到全矩阵代数的线性群逆保持

设F是一个特征不为2的域,Mn(F)和Sn(F)分别记F上的n×n全矩阵代数和对称矩阵代数.所有的从Sn(F)到Mn(F)的保群逆的线性映射被刻划,作为一个中间步骤,三个矩阵的同时相似标准形也被证明.这个标准形简化了从Sn(F)到Mn(F)的保群逆的线性映射的刻划.     

Additive maps preserving M-P inverses of matrices over Fields

Suppose F is a field of characteristic not 2 or 3. A characterization is given for all additive maps, on the algebra of all n × n matrices over F. which preserve Moore -Penrose(M-P) Inverses of matrices.