Contemporary Linear Algebra

ISBN-10: 0471163627

ISBN-13: 9780471163626

Edition: 2003

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Description:

From one of the premier authors in higher education comes a new linear algebra textbook that fosters mathematical thinking, problem-solving abilities, and exposure to real-world applications. Without sacrificing mathematical precision, Anton and Busby focus on the aspects of linear algebra that are most likely to have practical value to the student while not compromising the intrinsic mathematical form of the subject. Throughout Contemporary Linear Algebra, students are encouraged to look at ideas and problems from multiple points of view.
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Book details

List price: $246.95
Copyright year: 2003
Publisher: John Wiley & Sons, Incorporated
Publication date: 9/2/2002
Binding: Hardcover
Pages: 656
Size: 8.25" wide x 10.25" long x 1.25" tall
Weight: 3.432
Language: English

Vectors
Vectors and Matrices in Engineering and Mathematics
Dot Product and Orthogonality
Vector Equations of Lines and Planes
Systems of Linear Equations
Introduction to Systems of Linear Equations
Solving Linear Systems by Row Reduction
Applications of Linear Systems
Matrices and Matrix Algebra
Operations on Matrices
Inverses
Algebraic Properties of Matrices
Elementary Matrices
A Method for Finding A-1
Subspaces and Linear Independence
The Geometry of Linear Systems
Matrices with Special Forms
Matrix Factorizations
LU-Decomposition
Partitioned Matrices and Parallel Processing
Determinants
Determinants
Cofactor Expansion
Properties of Determinants
Cramer's Role
Formula for A-1
Applications of Determinants
A First Look at Eigenvalues and Eigenvectors
Matrix Models
Dynamical Systems and Markov Chains
Leontief Input-Output Models
Gauss-Seidel and Jacobi Iteration
Sparse Linear Systems
The Power Method
Application to Internet Search Engines
Linear Transformations
Matrices as Transformations
Geometry of Linear Operators
Kernel and Range
Composition and Invertibility of Linear Transformations
Computer Graphics
Dimension and Structure
Basis and Dimension
Properties of Bases
The Fundamental Spaces of a Matrix
The Dimension Theorem and Its Implications
The Rank Theorem and Its Implications
The Pivot Theorem and Its Implications
The Projection Theorem and Its Implications
Best Approximation and Least Squares
Orthonormal Bases and the Gram-Schmidt Process
QR-Decomposition
Householder Transformations
Coordinates with Respect to a Basis
Diagonalization
Matrix Representations of Linear Transformations
Similarity and Diagonalizability
Orthogonal Diagonalizability
Functions of a Matrix
Quadratic Forms
Application of Quadratic Forms to Optimization
Singular Value Decomposition
The Pseudoinverse
Complex Eigenvalues and Eigenvectors
Hermitian, Unitary, and Normal Matrices
Systems of Differential Equations
General Vector Spaces
Vector Space Axioms
Inner Product Spaces
Fourier Series
General Linear Transformations
Isomorphism
How to Read Theorems
Complex Numbers.Answers to Odd-Numbered Exercises.Photo Credits
Index
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