Elementary Linear Algebra

ISBN-10: 0471669601

ISBN-13: 9780471669609

Edition: 9th 2005 (Revised)

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Description: This classic treatment of linear algebra presents the fundamentals in the clearest possible way, examining basic ideas by means of computational examples and geometrical interpretation. It proceeds from familiar concepts to the unfamiliar, from the concrete to the abstract. Readers consistently praise this outstanding text for its expository style and clarity of presentation. Clear, accessible, step-by-step explanations make the material crystal clear. The authors spotlight the relationships between concepts to give a unified and complete picture. Established the intricate thread of relationships between systems of equations, matrices, determinants, vectors, linear transformations and eigenvalues.

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Book details

List price: $179.95
Edition: 9th
Copyright year: 2005
Publisher: John Wiley & Sons, Incorporated
Publication date: 12/27/2004
Binding: Hardcover
Pages: 624
Size: 8.00" wide x 10.00" long x 1.00" tall
Weight: 3.234
Language: English

Note: All relevant chapters end with Supplementary Exercises.
Linear Equations and Matrices
Systems of Linear Equations
Matrices
Matrix Multiplication
Algebraic Properties of Matrix Operations
Special Types of Matrices and Partitioned Matrices
Matrix Transformations
Computer Graphics
Correlation Coefficient (Optional)
Solving Linear Systems
Echelon Form of a Matrix
Elementary Matrices: Finding A-1
Equivalent Matrices
LU-Factorization (Optional)
Real Vector Spaces
Vectors in the Plane and in 3-space
Vector Spaces
Subspaces
Span and Linear Independence
Basis and Dimension
Homogeneous Systems
Coordinates and Isomorphisms
Rank of a Matrix
Inner Product Spaces
Standard Inner Product on R2 and R3
Cross Product in R3 (Optional)
Inner Product Spaces
Gram-Schmidt Process
Orthogonal Complements
Least Squares (Optional)
Linear Transformations and Matrices
Definition and Examples
Kernel and Range of a Linear Transformation
Matrix of a Linear Transformation
Vector Space of Matrices and Vector Space of Linear Transformations (Optional)
Similarity
Inroduction to Homogeneous Coordinates (Optional)
Determinants
Definition
Properties of Determinants
Cofactor Expansion
Inverse of a Matrix
Other Applications of Determinants
Determinants from a Computational Point of View
Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors
Diagonalization and Similar Matrices
Stable Age Distribution in a Population
Markov Processes (Optional)
Diagonalization of Symmetric Matrices
Spectral Decomposition and Singular Value Decomposition (Optional)
Real Quadratic Forms
Conic Sections
Quadric Surfaces
Dominant Eigenvalue and Principal Component Analysis (Optional)
Differential Equations (Optional)
Differential Equations
Dynamical Systems
MATLAB for Linear Algebra
Input and Output in MATLAB
Matrix Operations in MATLAB
Matrix Powers and Some Special Matrices
Elementary Row Operations in MATLAB
Matrix Inverses in MATLAB
Vectors in MATLAB
Applications of Linear Combinations in MATLAB
Linear Transformations in MATLAB
MATLAB Command Summary
MATLAB Exercises
Preliminaries Sets Functions
Complex Numbers Complex Numbers Complex Numbers in Linear Algebra
Introduction to Proofs
Answers to Odd-Numbered Exercises
Index
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