In this volume in his exceptional series of translations of Russian mathematical texts, Richard Silverman has taken Shilov’s course in linear algebra and has made it even more accessible and more useful for English language readers. Georgi E. Shilov, Professor of Mathematics at the Moscow State University, covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional algebras and their representations, with an appendix on categories of finite-dimensional spaces. The author begins with elementary material and goes easily into the advanced areas, covering all the standard topics of an advanced undergraduate or beginning graduate course. The material is presented in a consistently clear style. Problems are included, with a full section of hints and answers in the back. Keeping in mind the unity of algebra, geometry and analysis in his approach, and writing practically for the student who needs to learn techniques, Professor Shilov has produced one of the best expositions on the subject. Because it contains an abundance of problems and examples, the book will be useful for self-study as well as for the classroom.

In the spirit of the author’s Basic Language of Mathematics, this companion volume is a careful exposition of the concepts and processes of Linear Algebra. It stresses cautious and clear explanations, avoiding reliance on co–ordinates as much as possible, and with special, but not exclusive, attention to the finite–dimensional situation. It is intended to also serve as a conceptual and technical background for use in geometry and analysis as well as other applications.

A thorough first course in linear algebra, this two-part treatment begins with the basic theory of vector spaces and linear maps, including dimension, determinants, eigenvalues, and eigenvectors. The second section addresses more advanced topics such as the study of canonical forms for matrices. The treatment can be tailored to satisfy the requirements of both introductory and advanced courses. Introductory courses that also serve as an initiation into formal mathematics will focus on the first six chapters. Students already schooled in matrices and linear mappings as well as theorem-proving will quickly proceed to selected chapters from part two. The selection can emphasize algebra or analysis/geometry, as needed. Ample examples, applications, and exercises appear throughout the text, which is supplemented by three helpful Appendixes.

Linear Algebra constitutes a foundation course for those specializing in the fields of mathematics, engineering and science. The course normally takes one semester, but for those needing a more rigorous study of the subject, it involve up to two semesters.This book is based on the lecture notes given for the linear algebra course at the Department of Mathematics in Wuhan University.

A complete quick reference guide for all aspects of Linear Algebra.