Linear Algebra

by Georgi E. Shilov

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.

Genres: Mathematics, Nonfiction, Textbooks, Stem, Science, Reference, Algebra

400 pages, Paperback

First published January 1, 1971

Reviews

[Nathan Morgan · Rating 4 out of 5]

This was a solid text for an introduction to linear algebra. Shilov does a great job at introducing the main concepts of linear algebra in a logical sequence that is easy to comprehend. The book includes important, well demonstrated proofs that are easy to follow. The book includes practice problems with their solutions, which are useful for the reader's self-teaching.

[William Schram · Rating 5 out of 5]

Usually, I read advanced mathematics textbooks and float through the entire thing without grasping the meanings of the symbols. I found myself recognizing and remembering aspects of the subject with Linear Algebra by Georgi E. Shilov.

Long ago, I attended a college-level algebra course. The only difference is how the book displays the theorems. There were some points I forgot, such as matrices having ranks.

I enjoyed the book. Thanks for reading my review, and see you next time.

[Lucas · Rating 3 out of 5]

Essa foi a primeira vez que li esse livro. É muito bem organizado, mas, na maioria dos tópicos, quase não tem exemplo numérico, o que dificulta o self-study para pessoas como eu pouco afeitas a provas matemáticas.

Apesar disso, eu consegui absorver bem os primeiros 6 capítulos, mas desandei a partir de Coordinate Transforms. Resolvi voltar um pouco e estudar mais formalismo matemático e um livro mais básico de algébra linear antes de retornar a esse livro do Shilov.

Creio que consegui absorver os 6 primeiros capítulos por serem conteúdos que já fui exposto na universidade. Então não recomendaria esse livro como um primeiro livro de AL.

[Glenn · Rating 2 out of 5]

waste of time

Seems like a bargain, but the electronic version is riddled with typos. Would be hard to understand even if it was printed correctly..

[Matthew Meeker · Rating 5 out of 5]

This book is Linear Algebra kino.

[Martin]

I’ve tried reading this book 3 or 4 times now and I cannot make it past chapter 1. The rigor is intense and the learning curve is steep. I’m still hopeful that I can someday grasp this topic.

[Bradley Gram-hansen · Rating 3 out of 5]

Not my favourite on the subject.