En esta colección de ejercicios y problemas de Álgebra lineal se reúnen gran número de enunciados y soluciones esquemáticas de muchos de ellos. Determinantes. Sistemas de ecuaciones lineales. Matrice

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.

A completely reworked new edition of this superb textbook. This key work is geared to the needs of the graduate student. It covers, with proofs, the usual major branches of groups, rings, fields, and modules. Its inclusive approach means that all of the necessary areas are explored, while the level of detail is ideal for the intended readership. The text tries to promote the conceptual understanding of algebra as a whole, doing so with a masterful grasp of methodology. Despite the abstract subject matter, the author includes a careful selection of important examples, together with a detailed elaboration of the more sophisticated, abstract theories

Existen excelentes loibros para el estudio del álgebra lineal, pero ninguno se adapta a los contenidos previstos para un primer curso en la Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio de la Universidad Politecnica de Madrid. Esta publicacion es un punto de partida mas accesible porque busca adaptarse al curriculo del estudiante de primer curso de ingenieria.

This is a softcover reprint of the English translation of 1990 of the revised and expanded version of Bourbaki's, Algebre, Chapters 4 to 7 (1981). This completes Algebra, 1 to 3, by establishing the theories of commutative fields and modules over a principal ideal domain. Chapter 4 deals with polynomials, rational fractions and power series. A section on symmetric tensors and polynomial mappings between modules, and a final one on symmetric functions, have been added. Chapter 5 was entirely rewritten. After the basic theory of extensions (prime fields, algebraic, algebraically closed, radical extension), separable algebraic extensions are investigated, giving way to a section on Galois theory. Galois theory is in turn applied to finite fields and abelian extensions. The chapter then proceeds to the study of general non-algebraic extensions which cannot usually be found in textbooks: p-bases, transcendental extensions, separability criterions, regular extensions. Chapter 6 treats ordered groups and fields and based on it is Chapter 7: modules over a p.i.d. studies of torsion modules, free modules, finite type modules, with applications to abelian groups and endomorphisms of vector spaces.Sections on semi-simple endomorphisms and Jordan decomposition have been added.Chapter IV: Polynomials and Rational FractionsChapter V: Commutative FieldsChapter VI: Ordered Groups and FieldsChapter VII: Modules Over Principal Ideal Domains

Este libro constituye una introducción a los principios y fundamentos del álgebra, con particular énfasis en sus aplicaciones a la ingeniería y ciencias afines.El texto explica, cubriendo todos los temas desde el principio, los distintos elementos del algebra, tales como ecuaciones, factores y exponentes, continuando con progresiones sencillas y permutaciones. El curso se ha valorado cuidadosamente, y solo requiere, por parte del estudiante, nociones de aritmetica elemental. En cada capitulo se incluyen numerosos ejercicios (con soluciones), destinados a comprobar y estimular los progresos del lector.

Este volumen desarrolla el programa de la asignatura Algebra Lineal de primer curso de la ETSICCP de la UPV, tanto para la titulación de Ingeniería de Caminos como de Obras Públicas. El objetivo fundamental es exponer de manera conisa los elementos del álgebra lineal que el estudiante debe conocer y manejar, ya que su uso resultará imprescindible a lo largo de sus estudios así como en su posterior vida profesional. Se estructura en once capítulos. Los siete primeros abarcan el programa básico del curso. En ellos se justifican los resultados teóricos con argumentos constructivos que posibilitan la comprensión de los mismos. Se muestran también numerosos ejemplos y ejercicios resueltos, con el fin de que el estudiante domine y aplique con soltura los conceptos teóricos. Los cuatro últimos capítulos conforman un bloque de temas de ampliación, en el que se presentan resultados y aplicaciones del álgebra matricial a la resolución de sistemas diferenciales.

El profesor Sigler ha escrito un buen libro de iniciación al Álgebra, de línea moderna actualizada, y que es muy apto para un primer curso de esta disciplina en las Facultades de Ciencias.L. E. Sigler, Bucknell University, Lewisburg, Penn., EE. UU.

Algebra fulfills a definite need to provide a self-contained, one volume, graduate level algebra text that is readable by the average graduate student and flexible enough to accomodate a wide variety of instructors and course contents.The guiding philosophical principle throughout the text is that the material should be presented in the maximum usable generality consistent with good pedagogy. Therefore it is essentially self-contained, stresses clarity rather than brevity and contains an unusually large number of illustrative exercises.The book covers major areas of modern algebra, which is a necessity for most mathematics students in sufficient breadth and depth.