Linear Algebra and Matrix Theory / Edition 2

Hardcover (Print)
Buy Used
Buy Used from
(Save 39%)
Item is in good condition but packaging may have signs of shelf wear/aging or torn packaging.
Condition: Used – Good details
Used and New from Other Sellers
Used and New from Other Sellers
from $24.90
Usually ships in 1-2 business days
(Save 92%)
Other sellers (Hardcover)
  • All (9) from $24.90   
  • New (2) from $64.85   
  • Used (7) from $24.90   
Sort by
Page 1 of 1
Showing All
Note: Marketplace items are not eligible for any coupons and promotions
Seller since 2008

Feedback rating:



New — never opened or used in original packaging.

Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift.

Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage.

Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item.

Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item.

Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer.


Ships from: Chicago, IL

Usually ships in 1-2 business days

  • Standard, 48 States
  • Standard (AK, HI)
Seller since 2010

Feedback rating:


Condition: New
0534405819 HARDCOVER. NEW. Never used. We do not ship to PO Box/APO/FPO addresses.

Ships from: Cupertino, CA

Usually ships in 1-2 business days

  • Canadian
  • International
  • Standard, 48 States
  • Standard (AK, HI)
Page 1 of 1
Showing All
Sort by


Intended for a serious first course or a second course in linear algebra, this book carries students beyond eigenvalues and eigenvectors to the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices. The authors present the material from a structural point of view: fundamental algebraic properties of the entities involved are emphasized. The approach is particularly important because the mathematical systems encountered in linear algebra furnish a wealth of examples for the structures studied in more advanced courses. By taking a straight and smooth path to the heart of linear algebra, students will be able to make the transition from the intuitive developments of courses at a lower level to the more abstract treatments encountered later.

Audience: Undergraduate math majors who have some background in linear algebra and would benefit from a strong foundation for more abstract treatments at a higher level. Also serves as text for introductory courses.

Read More Show Less

Editorial Reviews

From the Publisher
"Jimmie and Linda Gilbert...present material at the appropriate level in a quick and concise manner....Some texts do not develop enough mathematical sophistication to enable the transition to junior- or senior-level linear algebra courses. The Gilbert text does!" "While the earlier edition of the Gilbert book was suitable for second and third year mathematics students, the level of writing was challenging for first year students. I was very pleased to find that the Gilberts have added a good number of meaningful examples and exercises at the appropriate level for such students. Moreover, in carefully doing so, they have not destroyed their crisp and efficient style of writing."

"I am...quite enthusiastic about the arrangement of topics which the Gilberts have chosen....The Gilberts Chapter 1 plays as a sort of overture, in which the main elements of vector space theory are laid out in a comfortable space, while due attention is paid to the role of computation. I think this type of start to a course would orient the students properly toward general vector space theory, rather than having them come upon the annoying complication of vector spaces after three or more weeks spent exclusively in computation and row reduction."

"The notation and terminology are clear and concise and the flow of topics and concepts is smooth."

"The material is well-written, it will be easy to teach from, and the students will find it easy to read and study from."

Read More Show Less

Product Details

  • ISBN-13: 9780534405816
  • Publisher: Cengage Learning
  • Publication date: 2/16/2004
  • Edition description: REV
  • Edition number: 2
  • Pages: 552
  • Product dimensions: 7.50 (w) x 9.40 (h) x 0.90 (d)

Meet the Author

Jimmie Gilbert was Professor of Mathematics at the University of South Carolina, Upstate. He received his Ph.D from Auburn University with a specialty in Linear and Abstract Algebras. He authored the first edition of Elements of Modern Algebra in 1970, joined on subsequent editions by his wife and longtime co-author Linda Gilbert. Together they have published titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, Intermediate Algebra, and another Cengage Learning title, Linear Algebra and Matrix Theory, now in its second edition. He and Linda have 6 children and 8 grandchildren. In his leisure time Jimmie enjoyed the outdoors, fishing, and gardening.

Linda Gilbert received her Ph.D. from Louisiana Tech University with a specialty in Linear and Abstract Algebras. She has been writing textbooks since 1981 with her husband Jimmie Gilbert, including ELEMENTS OF MODERN ALGEBRA and LINEAR ALGEBRA and MATRIX THEORY (now in its second edition) with Cengage Learning, plus titles in College Algebra, Precalculus, College Algebra and Trigonometry, Trigonometry, and Intermediate Algebra.

Read More Show Less

Table of Contents

1. REAL COORDINATE SPACES. The Vector Spaces Rn. Linear Independence. Subspaces of Rn. Spanning Sets. Geometric Interpretations of R² and R³. Bases and Dimension. 2. ELEMENTARY OPERATIONS ON VECTORS. Elementary Operations and Their Inverses. Elementary Operations and Linear Independence. Standard Bases for Subspaces. 3. MATRIX MULTIPLICATION. Matrices of Transition. Properties of Matrix Multiplication. Invertible Matrices. Column Operations and Column-Echelon Forms. Row Operations and Row-Echelon Forms. Row and Column Equivalence. Rank and Equivalence. LU Decompositions. 4. VECTOR SPACES, MATRICES, AND LINEAR EQUATIONS. Vector Spaces. Subspaces and Related Concepts. Isomorphisms of Vector Spaces. Standard Bases for Subspaces. Matrices over an Arbitrary Field. Systems of Linear Equations. More on Systems of Linear Equations. 5. LINEAR TRANSFORMATIONS. Linear Transformations. Linear Transformations and Matrices. Change of Basis. Composition of Linear Transformations. 6. DETERMINANTS. Permutations and Indices. The Definition of a Determinant. Cofactor Expansions. Elementary Operations and Cramer's Rule. Determinants and Matrix Multiplication. 7. EIGENVALUES AND EIGENVECTORS. Eigenvalues and Eigenvectors. Eigenspaces and Similarity. Representation by a Diagonal Matrix. 8. FUNCTIONS OF VECTORS. Linear Functionals. Real Quadratic Forms. Orthogonal Matrices. Reduction of Real Quadratic Forms. Classification of Real Quadratic Forms. Binlinear Forms. Symmetric Bilinear Forms. Hermitian Forms. 9. INNER PRODUCT SPACES. Inner Products. Norms and Distances. Orthonormal Bases. Orthogonal Complements. Isometrics. Normal Matrices. Normal Linear Operators. 10. SPECTRAL DECOMPOSITIONS. Projections and Direct Sums. Spectral Decompositions. Minimal Polynomials and Spectral Decompositions. Nilpotent Transformations. The Jordan Canonical Form. 11. NUMERICAL METHODS. Sequences and Series of Vectors. Sequences and Series of Matrices. The Standard Method of Iteration. Cimmino's Method. An Iterative Method for Determining Eigenvalues.

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)