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Elementary Linear Algebra A Matrix Approach

ISBN-10: 0137167229
ISBN-13: 9780137167227
Edition: 2000
List price: $134.00
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Description: For a sophomore-level course in Linear Algebra. Based on the recommendations of the LACSG, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications and less emphasis on abstraction  More...

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Book details

List price: $134.00
Copyright year: 2000
Publisher: Prentice Hall PTR
Publication date: 9/7/1999
Binding: Hardcover
Pages: 451
Size: 8.50" wide x 10.50" long x 1.00" tall
Weight: 2.442
Language: English

For a sophomore-level course in Linear Algebra. Based on the recommendations of the LACSG, this introduction to linear algebra offers a matrix-oriented approach with more emphasis on problem solving and applications and less emphasis on abstraction than in a traditional course. Throughout the text, use of technology is encouraged. The focus is on matrix arithmetic, systems of linear equations, properties of Euclidean n-space, eigenvalues and eigenvectors, and orthogonality. Although matrix-oriented, the text provides a solid coverage of vector spaces.

Preface
To the Student
Matrices, Vectors, and Systems of Linear Equations
Matrices and Vectors
Linear Combinations, Matrix-Vector Products, and Special Matrices
Systems of Linear Equations
Gaussian Elimination
Applications of Systems of Linear Equations
The Span of a Set of Vectors
Linear Dependence and Linear Independence
Review Exercises
Matrices and Linear Transformations
Matrix Multiplication
Applications of Matrix Multiplication
Invertibility and Elementary Matrices
The Inverse of a Matrix
The LU Decomposition of a Matrix
Linear Transformations and Matrices
Composition and Invertibility of Linear Transformations
Review Exercises
Determinants
Cofactor Expansion
Properties of Determinants
Review Exercises
Subspaces and Their Properties
Subspaces
Basis and Dimension
The Dimensions of Subspaces Associated with a Matrix
Coordinate Systems
Matrix Representations of Linear Operators
Review Exercises
Eigenvalues, Eigenvectors, and Diagonalization
Eigenvalues and Eigenvectors
The Characteristic Polynomial
Diagonalization of Matrices
Diagonalization of Linear Operators
Applications of Eigenvalues
Review Exercises
Orthogonality
The Geometry of Vectors
Orthogonal Vectors
Least-Squares Approximation and Orthogonal Projection Matrices
Orthogonal Matrices and Operators
Symmetric Matrices
Singular Value Decomposition
Rotations of R[superscript 3] and Computer Graphics
Review Exercises
Vector Spaces
Vector Spaces and Their Subspaces
Dimension and Isomorphism
Linear Transformations and Matrix Representations
Inner Product Spaces
Review Exercises
Complex Numbers
References
Answers to Odd-Numbered Exercises
Index

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