The Class Matrix

“A quite thorough and impressive work, not only a compelling defense of materialism but also a fair-minded if highly critical engagement with cultural theory. It isn’t clear how culturalists—especially the anti-Marxist ones—can effectively respond to this broadside, tightly and cogently argued as it is.”—Chris Wright, CounterPunch “Chibber...has developed a sophisticated, elegant, and readable defense of the sociological significance of class structure in understanding and addressing the key problems inherent in capitalism.”—Choice “[A] clear, compelling, and systematic statement of the view that class is an objective reality that predictably and rationally shapes human thought and action, one we need to grapple with seriously if we’re to comprehend contemporary society and its morbid symptoms.”—Jacobin Following the collapse of the Soviet Union, theorists argued that social and economic life is reducible to culture—that our choices reflect interpretations of the world around us rather than the limitations imposed by basic material facts. Today, gross inequalities in wealth and power have pushed scholars to reopen materialist lines of inquiry. But it would be a mistake to pretend that the cultural turn never happened. Vivek Chibber instead engages cultural theory seriously, proposing a fusion of materialism and the most useful insights of its rival. Chibber accommodates the main arguments from the cultural turn within a robust materialist framework, showing how one can agree that the making of meaning plays an important role in social agency while still recognizing the fundamental power of class structure and class formation. He vindicates classical materialism by demonstrating that it accounts for phenomena cultural theorists thought it was powerless to explain, while also showing that aspects of class are indeed centrally affected by cultural factors. The Class Matrix does not seek to displace culture from the analysis of modern capitalism. Rather, in prose of exemplary clarity, Chibber gives culture its due alongside what Marx called “the dull compulsion of economic relations.”

This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

The Matrix trilogy is unique among recent popular films in that it is constructed around important philosophical questions--classic questions which have fascinated philosophers and other thinkers for thousands of years. Editor Christopher Grau here presents a collection of new, intriguing essays about some of the powerful and ancient questions broached by The Matrix and its sequels, written by some of the most prominent and reputable philosophers working today. They provide intelligent, accessible, and thought-provoking examinations of the philosophical issues that support the films. Philosophers Explore The Matrix includes an introduction that surveys the use of philosophical ideas in the film. Topics that the contributors tackle include: how a collaborative dream could differ from hallucination, the difference between the Matrix and the "real" world; why living in the Matrix would be considered "bad"; the similarities between the Matrix and Plato's Cave; the moral status of artificially created beings, whether one can behave immorally in illusory circumstances, and the true nature of free will and responsibility. This volume also includes an appendix of classic philosophical writing on these issues by Plato, Berkeley, Descartes, Putnam, and Nozick. Philosophers Explore The Matrix will fascinate any fan of the films who wants to delve deeper into their themes, as well as any student of philosophy who desires an accessible entry into this challenging and profoundly vital world of ideas.

A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Several classes of matrices are thoroughly developed including the classes of matrices of 0's and 1's with a specified number of 1's in each row and column (equivalently, bipartite graphs with a specified degree sequence), symmetric matrices in such classes (equivalently, graphs with a specified degree sequence), tournament matrices with a specified number of 1's in each row (equivalently, tournaments with a specified score sequence), nonnegative matrices with specified row and column sums, and doubly stochastic matrices. Most of this material is presented for the first time in book format and the chapter on doubly stochastic matrices provides the most complete development of the topic to date.

The Kronecker product of matrices plays a central role in mathematics and in applications found in engineering and theoretical physics. These applications are signal processing, statistical physics, quantum groups and quantum computers. This book provides a comprehensive introduction to the Kronecker product of matrices together with its software implementation in C++ using an object-oriented design.

Matrix Analysis presents the classical and recent results for matrix analysis that have proved to be important to applied mathematics.

In recent years several new classes of matrices have been discovered and their structure exploited to design fast and accurate algorithms. In this new reference work, Raf Vandebril, Marc Van Barel, and Nicola Mastronardi present the first comprehensive overview of the mathematical and numerical properties of the family's newest member: semiseparable matrices. The text is divided into three parts. The first provides some historical background and introduces concepts and definitions concerning structured rank matrices. The second offers some traditional methods for solving systems of equations involving the basic subclasses of these matrices. The third section discusses structured rank matrices in a broader context, presents algorithms for solving higher-order structured rank matrices, and examines hybrid variants such as block quasiseparable matrices. An accessible case study clearly demonstrates the general topic of each new concept discussed. Many of the routines featured are implemented in Matlab and can be downloaded from the Web for further exploration.

This volume concisely presents fundamental ideas, results, and techniques in linear algebra and mainly matrix theory. Each chapter focuses on the results, techniques, and methods that are beautiful, interesting, and representative, followed by carefully selected problems. For many theorems several different proofs are given. The only prerequisites are a decent background in elementary linear algebra and calculus.

This monograph presents a collection of results, observations, and examples related to dynamical systems described by linear and nonlinear ordinary differential and difference equations. In particular, dynamical systems that are susceptible to analysis by the Liapunov approach are considered. The naive observation that certain "diagonal-type" Liapunov functions are ubiquitous in the literature attracted the attention of the authors and led to some natural questions. Why does this happen so often? What are the spe cial virtues of these functions in this context? Do they occur so frequently merely because they belong to the simplest class of Liapunov functions and are thus more convenient, or are there any more specific reasons? This monograph constitutes the authors' synthesis of the work on this subject that has been jointly developed by them, among others, producing and compiling results, properties, and examples for many years, aiming to answer these questions and also to formalize some of the folklore or "cul ture" that has grown around diagonal stability and diagonal-type Liapunov functions. A natural answer to these questions would be that the use of diagonal type Liapunov functions is frequent because of their simplicity within the class of all possible Liapunov functions. This monograph shows that, although this obvious interpretation is often adequate, there are many in stances in which the Liapunov approach is best taken advantage of using diagonal-type Liapunov functions. In fact, they yield necessary and suffi cient stability conditions for some classes of nonlinear dynamical systems.

Concise, masterly survey of a substantial part of modern matrix theory introduces broad range of ideas involving both matrix theory and matrix inequalities. Also, convexity and matrices, localization of characteristic roots, proofs of classical theorems and results in contemporary research literature, more. Undergraduate-level. 1969 edition. Bibliography.