Advanced Linear Algebra

  • Steven Roman

Part of the Graduate Texts in Mathematics book series (GTM, volume 135)

Table of contents

  1. Front Matter
    Pages I-XVIII
  2. Basic Linear Algebra

    1. Front Matter
      Pages 33-33
    2. Steven Roman
      Pages 35-58
    3. Steven Roman
      Pages 59-85
    4. Steven Roman
      Pages 87-107
    5. Steven Roman
      Pages 109-126
    6. Steven Roman
      Pages 127-138
    7. Steven Roman
      Pages 139-161
    8. Steven Roman
      Pages 163-184
    9. Steven Roman
      Pages 185-203
    10. Steven Roman
      Pages 205-226
    11. Steven Roman
      Pages 227-255
  3. Topics

    1. Front Matter
      Pages 257-257
    2. Steven Roman
      Pages 301-324
    3. Steven Roman
      Pages 325-353
    4. Steven Roman
      Pages 355-409
    5. Steven Roman
      Pages 427-441
    6. Steven Roman
      Pages 451-470
    7. Steven Roman
      Pages 471-506
  4. Back Matter
    Pages 507-526

About this book


For the third edition, the author has added a new chapter on associative algebras that includes the well known characterizations of the finite-dimensional division algebras over the real field (a theorem of Frobenius) and over a finite field (Wedderburn's theorem); polished and refined some arguments (such as the discussion of reflexivity, the rational canonical form, best approximations and the definitions of tensor products); upgraded some proofs that were originally done only for finite-dimensional/rank cases; added new theorems, including the spectral mapping theorem; considerably expanded the reference section with over a hundred references to books on linear algebra.

From the reviews of the second edition:

"In this 2nd edition, the author has rewritten the entire book and has added more than 100 pages of new materials....As in the previous edition, the text is well written and gives a thorough discussion of many topics of linear algebra and related fields...the exercises are rewritten and expanded....Overall, I found the book a very useful one....It is a suitable choice as a graduate text or as a reference book."

Ali-Akbar Jafarian, ZentralblattMATH

"This is a formidable volume, a compendium of linear algebra theory, classical and modern... The development of the subject is elegant...The proofs are neat...The exercise sets are good, with occasional hints given for the solution of trickier problems...It represents linear algebra and does so comprehensively."

Henry Ricardo, MAA Online


Eigenvalue Eigenvector algebra field linear algebra transformation

Authors and affiliations

  • Steven Roman
    • 1
  1. 1.8 Night StarIrvineUSA

Bibliographic information