Introduction to Linear Algebra, Second Edition (Undergraduate Texts in Mathematics)

Introduction to Linear Algebra, Second Edition (Undergraduate Texts in Mathematics)
~
Serge Lang

* Publisher: Springer
* Number Of Pages: 308
* Publication Date: 1997-03-14
* ISBN-10 / ASIN: 0387962050
* ISBN-13 / EAN: 9780387962054

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 are conceptual.

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Advanced Linear Algebra (Graduate Texts in Mathematics)

Advanced Linear Algebra (Graduate Texts in Mathematics)
by: Steven Roman

Details

# Hardcover: 526 pages
# Publisher: Springer; 3rd edition (October 8, 2007)
# Language: English
# ISBN-10: 0387728287
# ISBN-13: 978-0387728285

Description

This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with important applications.

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 and a theorem to the effect that , dim(V)<=dim(V*) with equality if and only if V is finite-dimensional; * corrected all known errors; * the reference section has been enlarged considerably, with over a hundred references to books on linear algebra.

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Linear Algebra and Its Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)

Linear Algebra and Its Applications (Pure and Applied Mathematics: A Wiley-Interscience Series of Texts, Monographs and Tracts)
by: Peter D. Lax

Details

# Hardcover: 392 pages
# Publisher: Wiley-Interscience; 2 edition (September 10, 2007)
# Language: English
# ISBN-10: 0471751561
# ISBN-13: 978-0471751564

Description

Praise for the First Edition

". . .recommended for the teacher and researcher as well as for graduate students. In fact, [it] has a place on every mathematician's bookshelf." -American Mathematical Monthly

Linear Algebra and Its Applications, Second Edition presents linear algebra as the theory and practice of linear spaces and linear maps with a unique focus on the analytical aspects as well as the numerous applications of the subject. In addition to thorough coverage of linear equations, matrices, vector spaces, game theory, and numerical analysis, the Second Edition features student-friendly additions that enhance the book's accessibility, including expanded topical coverage in the early chapters, additional exercises, and solutions to selected problems.

Beginning chapters are devoted to the abstract structure of finite dimensional vector spaces, and subsequent chapters address convexity and the duality theorem as well as describe the basics of normed linear spaces and linear maps between normed spaces.

Further updates and revisions have been included to reflect the most up-to-date coverage of the topic, including:

* The QR algorithm for finding the eigenvalues of a self-adjoint matrix
* The Householder algorithm for turning self-adjoint matrices into tridiagonal form
* The compactness of the unit ball as a criterion of finite dimensionality of a normed linear space

Additionally, eight new appendices have been added and cover topics such as: the Fast Fourier Transform; the spectral radius theorem; the Lorentz group; the compactness criterion for finite dimensionality; the characterization of commentators; proof of Liapunov's stability criterion; the construction of the Jordan Canonical form of matrices; and Carl Pearcy's elegant proof of Halmos' conjecture about the numerical range of matrices.

Clear, concise, and superbly organized, Linear Algebra and Its Applications, Second Edition serves as an excellent text for advanced undergraduate- and graduate-level courses in linear algebra. Its comprehensive treatment of the subject also makes it an ideal reference or self-study for industry professionals.

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Linear Algebra and Its Applications

Linear Algebra and Its Applications
by: Gilbert Strang

Details

# Hardcover: 496 pages
# Publisher: Brooks Cole; 4th edition (July 19, 2005)
# Language: English
# ISBN-10: 0030105676

Description

Renowned professor and author Gilbert Strang demonstrates that linear algebra is a fascinating subject by showing both its beauty and value. While the mathematics is there, the effort is not all concentrated on proofs. Strang's emphasis is on understanding. He explains concepts, rather than deduces. This book is written in an informal and personal style and teaches real mathematics. The gears change in Chapter 2 as students reach the introduction of vector spaces. Throughout the book, the theory is motivated and reinforced by genuine applications, allowing pure mathematicians to teach applied mathematics.

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