[신간의 별자리x] 우리/미술, 그리고 ‘슬픔의 박물관’

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.

A first course in noncommutative rings, by T. Y. Lam. Pp. 385. £37 (pb), £62.50 (hb). 2001. ISBN 0 387 95325 6 (pb), 0 387 95183 0 (hb) (Springer-Verlag).

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.

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Computational Methods for Linear Matrix Equations

$$\\left[ {\\begin{array}{*{20}{c}} {10} \\\\ { - v{{a}^{{ - 1}}}1} \\\\ \\end{array} } \\right]\\left[ {\\begin{array}{*{20}{c}} {au} \\\\ {vb} \\\\ \\end{array} } \\right]\\left[ {\\begin{array}{*{20}{c}} {1 - {{a}^{{ - 1}}}u} \\\\ {01} \\\\ \\end{array} } \\right] = \\left[ {\\begin{array}{*{20}{c}} {a0} \\\\ {0b - v{{a}^{{ - 1}}}u} \\\\ \\end{array} } \\right]$$ \n \n(1.1) \n \nprovided a is regular.

Determinants and matrices. By A. C. Aitken. Pp. vii, 135. 4s. 6d. 1939. University Mathematical Texts, 1. (Oliver and Boyd)

Quantum coherence and geometric quantum discord

Ranks and the least-norm of the general solution to a system of quaternion matrix equations

A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity

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.

Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations

A system of real quaternion matrix equations with applications

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.

Qing-Wen Wang

Papers

Ranks and the least-norm of the general solution to a system of quaternion matrix equations

A system of matrix equations and a linear matrix equation over arbitrary regular rings with identity

Bisymmetric and centrosymmetric solutions to systems of real quaternion matrix equations

A system of real quaternion matrix equations with applications

The general solution to a system of real quaternion matrix equations