[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.

/pdf/computational-methods-for-linear-matrix-equations-29c8rmvfvt.pdf

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

Minimal ranks of some quaternion matrix expressions with applications

A system of matrix equations with five variables

In this paper, we investigate the least-squares solution with the least norm to the following system of tensor equations over quaternions A 1 ∗ N X = D 1 , Y ∗ N B 2 = D 2 , A 3 ∗ N X ∗ N B 3 = D 3...

The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra

In this article, we consider the nonlinear matrix equation arising in an interpolation problem. We use the Thompson metric to prove that the matrix equation always has a unique positive definite solution. An iterative method is constructed to compute the unique positive definite solution and its error estimation formula is given. Based on the matrix differentiation, we give a precise perturbation bound for the unique positive definite solution. The new results are illustrated by some numerical examples in the end.

On the matrix equation arising in an interpolation problem

We in this paper derive the expression of the least square solution with the least norm to the system of generalized Sylvester quaternion matrix equations $$\begin{aligned} A_1X = E_1 ,\quad XB_1 = E_2, \quad C_1Y = E_3 ,\quad YD_1 = E_4,\quad A_2XB_2+C_2YD_2=E_5, \end{aligned}$$
 where X, Y are unknown quaternion matrices and the others are given quaternion matrices.

Qing-Wen Wang

Papers

Minimal ranks of some quaternion matrix expressions with applications

A system of matrix equations with five variables

The least-squares solution with the least norm to a system of tensor equations over the quaternion algebra

On the matrix equation arising in an interpolation problem

The Least Square Solution with the Least Norm to a System of Quaternion Matrix Equations