Introduction to Linear Algebra

by Serge Lang

This book is a short text in linear algebra, intended for a one-term course. In the first chapter, Lang discusses the relation between the geometry and the algebra underlying the subject, and gives concrete examples of the notions which appear later in the book. He then starts with a discussion of linear equations, matrices and gaussian elimination, and proceeds to discuss vector spaces, linear maps, scalar products, determinants, and eigenvalues. The book contains a large number of exercises, some of the routine computational type, and others more conceptual.

Genres: Mathematics, Textbooks, Algebra

293 pages, Hardcover

First published January 1, 1970

About the author

Serge Lang was an influential mathematician in the field of number theory. Algebra is his most famous book.

Librarian Note: There is more than one author in the GoodReads database with this name. See this thread for more information.

Reviews

[Lime Street Labrador · Rating 3 out of 5]

Introduction to fundamental concepts without digressing into non-core topics, but a few topics such as change of basis and similarity are poorly introduced while topics such as determinants and eigenvectors are better learned from other books.

[alsene · Rating 5 out of 5]

A very wonderful read, the topics are presened in a concise manner with a proper notation that makes the proofs very easy to follow.
Though I feel that the chapter on eigenvalues and eigenvectors wasn't very motivated, for the proofs could have been a little better, and I specifically complain about his proof for the fact that all symmetric linear mappings have orthogonal eigenvectors.
I also enjoyed his brief treatment on quadratic forms.
Overall an amazing book for an undergraduate aspiring to learn higher mathematics.

[Chris Herdt]

Professor John Johnstone recommended this text, among several, as a good way to remember the linear algebra I've forgotten since 1994.