Author
Qing-Wen Wang
Other affiliations: Nanyang Technological University, University of Wyoming, University of Science and Technology of China
Bio: Qing-Wen Wang is an academic researcher from Shanghai University. The author has contributed to research in topics: Matrix (mathematics) & Quaternion. The author has an hindex of 33, co-authored 148 publications receiving 2929 citations. Previous affiliations of Qing-Wen Wang include Nanyang Technological University & University of Wyoming.
Papers published on a yearly basis
Papers
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TL;DR: Wang et al. as mentioned in this paper established a new expression of the general solution to the consistent system of linear quaternion matrix equations A1X1=C1, A2X2=C2, A3X1B1+A4X2B2 =C3.
138 citations
TL;DR: In this article, the classical system of matrix equations A 1 XB 1 =C 1, A 2 XB 2 =C 2 over R, an arbitrary regular ring with identity, is considered.
136 citations
TL;DR: In this paper, the authors considered bisymmetric and centrosymmetric solutions to certain matrix equations over real quaternion algebra @? and obtained necessary and sufficient conditions for the matrix equation AX = C.
Abstract: In this paper we consider bisymmetric and centrosymmetric solutions to certain matrix equations over the real quaternion algebra @?. Necessary and sufficient conditions are obtained for the matrix equation AX = C and the following systemsA"1X=C"1,A"1X=C"1,XB"3=C"3,A"2X=C"2, to have bisymmetric solutions, and the systemA"1X=C"1,A"3XB"3=C"3, to have centrosymmetric solutions. The expressions of such solutions of the matrix and the systems mentioned above are also given. Moreover a criterion for a quaternion matrix to be bisymmetric is established and some auxiliary results on other sets over @? are also mentioned.
132 citations
TL;DR: In this article, the authors studied the problem of finding a (P, Q )-symmetric solution to a linear real quaternion matrix equation and provided necessary and sufficient conditions for the existence of a solution.
119 citations
TL;DR: In this paper, a necessary and sufficient condition for the existence and the expression of the general solution to the system of matrix equations over real quaternion algebra @? is given.
Abstract: In this paper, we consider the system of matrix equations, A"1X = C"1, A"2X = C"2, A"3XB"3 = C"3, and A"4XB"4 = C"4, over the real quaternion algebra @?. A necessary and sufficient condition for the existence and the expression of the general solution to the system are given. As particular cases, the corresponding results on other systems over @? are also obtained.
115 citations
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TL;DR: In this paper, a text on rings, fields and algebras is intended for graduate students in mathematics, aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation.
Abstract: This text, drawn from the author's lectures at the University of California at Berkeley, is intended as a textbook for a one-term course in basic ring theory. The material covered includes the Wedderburn-Artin theory of semi-simple rings, Jacobson's theory of the radical representation theory of groups and algebras, prime and semi-prime rings, primitive and semi-primitive rings, division rings, ordered rings, local and semi-local rings, and perfect and semi-perfect rings. By aiming the level of writing at the novice rather than at the expert, and by stressing the role of examples and motivation, the author has produced a text which is suitable not only for use in a graduate course, but also for self-study by other interested graduate students. Numerous exercises are also included. This graduate textbook on rings, fields and algebras is intended for graduate students in mathematics.
1,479 citations
TL;DR: The aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems, which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing.
Abstract: Given the square matrices $A, B, D, E$ and the matrix $C$ of conforming dimensions, we consider the linear matrix equation $A{\mathbf X} E+D{\mathbf X} B = C$ in the unknown matrix ${\mathbf X}$. Our aim is to provide an overview of the major algorithmic developments that have taken place over the past few decades in the numerical solution of this and related problems, which are producing reliable numerical tools in the formulation and solution of advanced mathematical models in engineering and scientific computing.
451 citations
TL;DR: In this paper, the authors show that if a is regular, then the ratio of 1.1 (n
(1.1) √ n (1)
√ 1.
Abstract: $$\\left[ {\\begin{array}{*{20}{c}} {10} \\\\ { - v{{a}^{{ - 1}}}1} \\\\ \\end{array} } \\right]\\left[ {\\begin{array}{*{20}{c}} {au} \\\\ {vb} \\\\ \\end{array} } \\right]\\left[ {\\begin{array}{*{20}{c}} {1 - {{a}^{{ - 1}}}u} \\\\ {01} \\\\ \\end{array} } \\right] = \\left[ {\\begin{array}{*{20}{c}} {a0} \\\\ {0b - v{{a}^{{ - 1}}}u} \\\\ \\end{array} } \\right]$$
(1.1)
provided a is regular.
386 citations
TL;DR: This aim is to provide a full review about the resource theory of quantum coherence, including its application in many-body systems, and the discordlike quantum correlations which were defined based on the various distance measures of states.
317 citations