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38 results on '"Zhang, Daochang"'

2. Jordan left derivations in infinite matrix rings

Author

Zhang Daochang, Ma Leiming, Hu Jianping, and Sun Chaochao

Subjects
left derivations, jordan left derivations, column finite matrix rings, infinite upper triangular matrix rings, 15b33, 16w25, 16s50, Mathematics, QA1-939
Abstract

Let RR be a unital associative ring. Our motivation is to prove that left derivations in column finite matrix rings over RR are equal to zero and demonstrate that a left derivation d:T→Td:{\mathcal{T}}\to {\mathcal{T}} in the infinite upper triangular matrix ring T{\mathcal{T}} is determined by left derivations dj{d}_{j} in R(j=1,2,…)R\left(j=1,2,\ldots ) satisfying d((aij))=(bij)d\left(\left({a}_{ij}))=\left({b}_{ij}) for any (aij)∈T\left({a}_{ij})\in {\mathcal{T}}, where bij=dj(a11),i=1,0,i≠1.{b}_{ij}=\left\{\begin{array}{ll}{d}_{j}\left({a}_{11}),& i=1,\\ 0,& i\ne 1.\end{array}\right. The similar results about Jordan left derivations are also obtained when RR is 2-torsion free.

Published
2024
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8. Weighted weak group inverse for Hilbert space operators

Author

Mosic, Dijana and Zhang, Daochang

Subjects
Mathematics - Functional Analysis, Mathematics - Operator Algebras
Abstract

We present the weighted weak group inverse, which is a new generalized inverse of operators between two Hilbert spaces, introduced to extend weak group inverse for square matrices. Some characterizations and representations of the weighted weak group inverse are investigated. We also apply these results to define and study the weak group inverse for a Hilbert space operator. Using the weak group inverse, we define and characterize various binary relations.

Published
2019

9. On the existence of group inverses of Peirce corner matrices

Author

Zhang, Daochang, Mosic, Dijana, and Tam, Tin-Yau

Subjects
Mathematics - Rings and Algebras
Abstract

We give some statements that are equivalent to the existence of group inverses of Peirce corner matrices of a $2 \times 2$ block matrix and its generalized Schur complements. As applications, several new results for the Drazin inverses of the generalized Schur complements and the $2 \times 2$ block matrix are obtained and some of them generalize several results in the literature.

Published
2018

12. On the generalized Drazin inverse of the sum in a Banach algebra

Author

Mosic, Dijana and Zhang, Daochang

Subjects
Mathematics - Functional Analysis
Abstract

The objective of this paper is to study the existence of the generalized Drazin inverse of the sum $a+b$ in a Banach algebra and present explicit expressions for the generalized Drazin inverse of this sum, under new conditions.

Published
2018

13. Drazin inverses of the sum of four matrices and its applications

Author

Zhang, Daochang, c, Dijana Mosi\', and Guo, Li

Subjects
Mathematics - Rings and Algebras
Abstract

Our aim is to establish relations between Drazin inverses of the pesudo-block matrix $(P,Q,R,S)$ and the block matrix composed of $P,R,S,Q$, where $R^2=S^2=0$. Based on the relations, we give representations for Drazin inverses of the sum $P+Q+R+S$ under weaker restrictions. As its applications, several expressions for Drazin inverses of a $2\times 2$ block matrix are presented under some assumptions. Our results generalize several results in the literature.

Published
2017

18. Representations for the Drazin inverse of the generalized Schur complement

Author

Zhang, Daochang and Du, Xiankun

Subjects
Mathematics - Rings and Algebras, 15A09, 65F20
Abstract

In this paper we present expressions for the Drazin inverse of the generalized Schur complement $A-CD^{d}B$ in terms of the Drazin inverses of $A$ and the generalized Schur complement $D-BA^{d}C$ under less and weaker restrictions, which generalize several results in the literature and the formula of Sherman-Morrison-Woodbury type.

Published
2013

20. Measure for Semantics and Semantically Constrained Pose Optimization: A Review

Author

Xia, Linlin, Li, Sida, Yi, Linna, Ruan, Heng, and Zhang, Daochang

Abstract

Simultaneous localization and mapping (SLAM) in robotics is a fundamental problem. The use of visual odometry (VO) enhances scene recognition in the task of ego-localization within an unknown environment. Semantically meaningful information permits data association and dense mapping to be conducted based on entities representing landmarks rather than manually designed, low-level geometric clues and has inspired various feature descriptors for semantically ensembled SLAM applications. This article illuminates the insights into the measure for semantics and the semantically constrained pose optimization. The concept of semantic extractor and the matched framework are initially presented. As the latest advances in computer vision and the learning-based deep feature acquisition are closely related, the semantic extractor is especially described in a deep learning paradigm. The methodologies pertinent to our explorations for object association and semantics-fused constraining that is amenable for use in a least-squares framework are summarized in a systematic way. By a collection of problem formulations and principle analyses, our review exhibits a fairly unique perspective in semantic SLAM. We further discuss the challenges of semantic uncertainty and explicitly introduce the term “semantic reasoning.” Some technology outlooks regarding semantic reasoning are simultaneously given. We argue that for intelligent tasks of robots such as object grasping, dynamic obstacle avoidance, and object-target navigation, semantic reasoning might guide the complex scene understanding under the framework of semantic SLAM directly to a solution.

Published
2024
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34. The Drazin inverse of the sum of four matrices and its applications.

Author

Zhang, Daochang, Mosić, Dijana, and Guo, Li

Subjects
*MATRICES (Mathematics), *MATRIX inversion
Abstract

Our aim is to establish relations between the Drazin inverses of the pesudo-block matrix (P , Q , R , S) and the block matrix P R S Q , where R 2 = S 2 = 0. Based on the relations, we give representations for the Drazin inverse of the sum P + Q + R + S under mild restrictions. As the applications, several expressions for the Drazin inverse of a 2 × 2 block matrix are presented under some assumptions. Our results generalize several results in the literature. [ABSTRACT FROM AUTHOR]

Published
2020
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35. On the Generalized Drazin inverse of the Sum in a Banach Algebra.

Author

Mosić, Dijana and Zhang, Daochang

Subjects
*BANACH algebras
Abstract

The objective of this paper is to study the existence of the generalized Drazin inverse of the sum a + b of two generalized Drazin invertible elements in a Banach algebra and present explicit expressions for the generalized Drazin inverse of this sum, under new conditions. [ABSTRACT FROM AUTHOR]

Published
2019
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