Linear Algebra and Matrix Theory / Edition 2

by Jimmie Gilbert, Linda Gilbert

Overview

Intended for a serious first course or a second course, this text will carry students beyond eigenvalues and eigenvectors to the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices. For this second edition, the authors, both affiliated with the University of South Carolina, have slowed the pace in the early chapters, and have added a new chapter on numerical methods, plus 46 new examples and 881 new exercises. The text is suitable for a one-year undergraduate course for mathematics majors. Annotation ©2004 Book News, Inc., Portland, OR

Product Details

ISBN-13:	9780534405816
Publisher:	Cengage Learning
Publication date:	02/16/2004
Edition description:	REV
Pages:	552
Product dimensions:	7.50(w) x 9.40(h) x 0.90(d)

About 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.

Table of Contents

Real Coordinate Spaces: The Vector Spaces R[super]n. Subspaces of R[super]n. Geometric Interpretations of R[super]2 and R[super]3. Bases and Dimension. Elementary Operations on Vectors: Elementary Operations and Their Inverses. Elementary Operations and Linear Independence. Standard Bases for Subspaces. Matrix Multiplication: Matrices of Transition. Properties of Matrix Multiplication. Invertible Matrices. Column Operationsand Column-Echelon Forms. Row Operations and Row-Echelon Forms. Row and Column Equivalence. Rank and Equivalence. 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. Linear Transformations: Linear Transformations. Linear Transformations and Matrices. Change of Basis. Composition of Linear Transformations. Determinants: Permutations and Indices. The Definition of a Determinant. Cofactor Expansions. Elementary Operations and Cramer's Rule. Determinants and Matrix Multiplication. Eigenvalues and Eigenvectors: Eigenvalues and Eigenvectors. Eigenspaces and Similarity. Representation by a Diagonal Matrix. Functions of Vectors: Linear Functionals. Real Quadratic Forms. Orthogonal Matrices. Reduction of Real Quadratic Forms. Classification of Real Quadratic Forms. Bilinear Forms. Symmetric Bilinear Forms. Hermitian Forms. Inner Product Spaces: Inner Products. Norms and Distances. Orthonormal Bases. Orthogonal Complements. Isometries. Normal Matrices. Normal Linear Operators. Spectral Decompositions: Projections and Direct Sums. Spectral Decompositions. Minimal Polynomials and Spectral Decompositions. Nilpotent Transformations. The Jordan Canonical Form. Index.

Editorial Reviews

"...the material is well-written, it will be easy to teach from, and the students will find it easy to read and study from."
-Jackie Garner, University of Arkansas
"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!"
—Melvyn Jeter, Illinois WesleyanUniversity
"The notation and terminology are clear and concise and the flow of topics and concepts is smooth."
-Ed Dixon, Tennessee Technological University
"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."
-Edward Hinson, University of New Hampshire

From the Publisher