Libros de Álgebra, página 7 de 28

This book presents a substantial part of matrix analysis that is functional analytic in spirit. Topics covered include the theory of majorization, variational principles for eigenvalues, operator monotone and convex functions, and perturbation of matrix functions and matrix inequalities. The book offers several powerful methods and techniques of wide applicability, and it discusses connections with other areas of mathematics.

Los métodos de Álgebra lineal, además de ser fundamentales en el desarrollo de otras partes de la Matemática, de la Estadística y de la Econometría, tienen una aplicación directa en los análisis económicos que se realizan de acuerdo con los modelos lineales. Esta pluralidad de funciones ha sido tenida en cuenta en esta obra en la cual se recogen además de los temas clásicos, cuestiones como la existencia de soluciones no negativas en un sistema lineal, de gran interés en los análisis económicos a causa de la naturaleza de las variables económicas, especialmente en los análisis input-output. Con una parte teórica suficiente y ejemplificada, se resuelven un gran número de ejercicios que, en algún caso, aclara cuestiones concretas.

This proceedings book brings selected works from two conferences, the 2nd Brazil-Mexico Meeting on Singularity and the 3rd Northeastern Brazilian Meeting on Singularities, that were hold in Salvador, in July 2015. All contributions were carefully peer-reviewed and revised, and cover topics like Equisingularity, Topology and Geometry of Singularities, Topological Classification of Singularities of Mappings, and more. They were written by mathematicians from several countries, including Brazil, Spain, Mexico, Japan and the USA, on relevant topics on Theory of Singularity, such as studies on deformations, Milnor fibration, foliations, Catastrophe theory, and myriad applications. Open problems are also introduced, making this volume a must-read both for graduate students and active researchers in this field.

This is a comprehensive textbook on modern algebra written by an internationally renowned specialist. It covers material traditionally found in advanced undergraduate and basic graduate courses and presents it in a lucid style. The author includes almost no technically difficult proofs, and reflecting his point of view on mathematics, he tries wherever possible to replace calculations and difficult deductions with conceptual proofs and to associate geometric images to algebraic objects.The effort spent on the part of students in absorbing these ideas will pay off when they turn to solving problems outside of this textbook. Another important feature is the presentation of most topics on several levels, allowing students to move smoothly from initial acquaintance with the subject to thorough study and a deeper understanding. Basic topics are included, such as algebraic structures, linear algebra, polynomials, and groups, as well as more advanced topics, such as affine and projective spaces, tensor algebra, Galois theory, Lie groups, and associative algebras and their representations. Some applications of linear algebra and group theory to physics are discussed. The book is written with extreme care and contains over 200 exercises and 70 figures. It is ideal as a textbook and also suitable for independent study for advanced undergraduates and graduate students.

Golovina

This textbook treats Lie groups, Lie algebras and their representations in an elementary but fully rigorous fashion requiring minimal prerequisites. In particular, the theory of matrix Lie groups and their Lie algebras is developed using only linear algebra, and more motivation and intuition for proofs is provided than in most classic texts on the subject.

Este libro, dirigido en particular a los alumnos de los primeros cursos de Ingeniería Técnica y de primer ciclo de Ingenierías Superiores, está totalmente actualizado y se ha elaborado de acuerdo con los nuevos planes de estudio. La obra surge ante la necesidad docente de ofrecer una visión global del conocimiento y paliar así una posible percepción de las asignaturas como compartimentos estancos, así como de evitar las posibles disfunciones y solapamientos que se producen tradicionalmente cuando se muestran los mismos conceptos en diferentes asignaturas. El criterio que se ha adoptado para estructurarlo ha sido el de agrupar las distintas asignaturas en unidades temáticas estrechamente relacionadas entre sí, acompañadas de una práctica conjunta final donde se utilizan los conceptos explicados. Gracias a la novedad que presenta el tratamiento secuenciado y conjunto de los temas de las diferentes materias ofrece la posibilidad de elegir distintos itinerarios, por asignaturas o por unidades temáticas, cumpliendo así una doble función, ya que no sólo puede utilizarse como libro base en cada una de las asignaturas, sino también como manual de consulta por temas.