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Linear Algebra and Matrix Theory

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ISBN-10: 0534405819

ISBN-13: 9780534405816

Edition: 2nd 2005 (Revised)

Authors: Jimmie Gilbert, Linda Gilbert

List price: $313.95
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Master linear algebra with LINEAR ALGEBRA AND MATRIX THEORY! With coverage of the classification of bilinear forms, normal matrices, spectral decompositions, the Jordan form, and sequences and series of matrices, this mathematics text prepares you to succeed in this course and in math courses in your future. Numerous examples and exercises illustrate the theories and provide you with the practice you need to master difficult concepts.
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Book details

List price: $313.95
Edition: 2nd
Copyright year: 2005
Publisher: Brooks/Cole
Publication date: 2/16/2004
Binding: Hardcover
Pages: 544
Size: 7.50" wide x 9.25" long x 1.00" tall
Weight: 2.222
Language: English

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.

Real Coordinate Spaces
The Vector Spaces Rn
Linear Independence
Subspaces of Rn
Spanning Sets
Geometric Interpretations of R? and R?
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 Operations and Column-Echelon Forms
Row Operations and Row-Echelon Forms
Row and Column Equivalence
Rank and Equivalence
LU Decompositions
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
Linear Transformations
Linear Transformations
Linear Transformations and Matrices
Change of Basis
Composition of Linear Transformations
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
Binlinear Forms
Symmetric Bilinear Forms
Hermitian Forms
Inner Product Spaces
Inner Products
Norms and Distances
Orthonormal Bases
Orthogonal Complements
Normal Matrices
Normal Linear Operators
Spectral Decompositions
Projections and Direct Sums
Spectral Decompositions
Minimal Polynomials and Spectral Decompositions
Nilpotent Transformations
The Jordan Canonical Form
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