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Linear Algebra (Undergraduate Texts in Mathematics)

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Linear Algebra (Undergraduate Texts in Mathematics) Cover

ISBN13: 9780387984551
ISBN10: 0387984550
Condition:
All Product Details

 

Synopses & Reviews

Publisher Comments:

This popular and successful text was originally written for a one-semester course in linear algebra at the sophomore undergraduate level. Students at this level generally have had little contact with complex numbers or abstract mathematics, so the book deals almost exclusively with real finite dimensional vector spaces, but in a setting and formulation that permits easy generalization to abstract vector spaces. The goal of the first two editions was the principal axis theorem for real symmetric linear transformation. The principal axis theorem becomes the first of two goals for this new edition, which follows a straight path to its solution. A wide selection of examples of vector spaces and linear transformation is presented to serve as a testing ground for the theory. In the second edition, a new chapter on Jordan normal form was added which reappears here in expanded form as the second goal of this new edition, along with applications to differential systems. To achieve the principal axis theorem in one semester a straight path to these two goals is followed. As compensation, there is a wide selection of examples and exercises. In addition, the author includes an introduction to invariant theory to show students that linear algebra alone is not capable of solving these canonical forms problems. The book continues to offer a compact, but mathematically clean introduction to linear algebra with particular emphasis on topics that are used in abstract algebra, the theory of differential equations, and group representation theory.

Synopsis:

Now in its third edition, this well-written book deals almost exclusively with real finite-dimensional vector spaces, but in a setting and formulation that permits easy generalization to abstract vector spaces. The book offers a compact and mathematically clean introduction to linear algebra with particular emphasis on topics that are used in the theory of differential equations. 23 illus.

Table of Contents

1: Vectors in the Plane and Space. 2: Vector Spaces. 3: Examples of Vector Spaces. 4: Subspaces. 5: Linear Independence and Dependence. 6: Finite Dimensional Vector Spaces and Bases. 7: The Elements of Vector Spaces: A Summing Up. 8: Linear Transformations. 9: Linear Transformations: Examples and Applications. 10: Linear Transformations and Matrices. 11: Representing Linear Transformations by Matrices. 12: More on Representing Linear Transformations by Matrices. 13: Systems of Linear Equations. 14: The Elements of Eigenvalue and Eigenvector Theory. 15: Inner Product Spaces. 16: The Spectral Theorem and Quadratic Forms. 17: Jordan Canonical Form. 18: Application to Differential Equations. 19: The Similarity Problem. Appendix A: Multilinear Algebra and Determinants. B: Complex Numbers.

What Our Readers Are Saying

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Average customer rating based on 1 comment:

rameshbrn, November 25, 2011 (view all comments by rameshbrn)
A great improvement over the 2nd edition, which was already lucidly written and was excellent for a 1-sem or 2-sem course in Linear Algebra
The 3rd edition makes a rational improvement in some chapters, gives miore importance to function space, dals with more applications.
The next edition must touch upon the historical aspect and the mathematicians involved the discovery and growth of the subject.
This book is both a text book for treatment & a reference book.
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Product Details

ISBN:
9780387984551
Author:
Smith, Larry
Author:
Smith, L.
Publisher:
Springer
Location:
New York :
Subject:
Algebra - Linear
Subject:
Algebras, linear
Subject:
Algebra
Subject:
Lineare Algebra
Subject:
Linear and Multilinear Algebras, Matrix Theory
Subject:
Mathematics-Linear Algebra
Copyright:
Edition Number:
3
Edition Description:
3rd ed. 1998
Series:
Undergraduate Texts in Mathematics
Publication Date:
19980528
Binding:
HARDCOVER
Language:
English
Illustrations:
Yes
Pages:
466
Dimensions:
235 x 155 mm 1840 gr

Related Subjects

Engineering » Mechanical Engineering » General
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Algebra » Linear Algebra
Science and Mathematics » Physics » General

Linear Algebra (Undergraduate Texts in Mathematics) New Hardcover
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$82.75 In Stock
Product details 466 pages Springer-Verlag - English 9780387984551 Reviews:
"Synopsis" by , Now in its third edition, this well-written book deals almost exclusively with real finite-dimensional vector spaces, but in a setting and formulation that permits easy generalization to abstract vector spaces. The book offers a compact and mathematically clean introduction to linear algebra with particular emphasis on topics that are used in the theory of differential equations. 23 illus.
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