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Elementary Linear Algebra with Applications

ISBN-10: 0030103479
ISBN-13: 9780030103476
Edition: 3rd 1996 (Revised)
Authors: Richard Hill
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Book details

List price: $331.95
Edition: 3rd
Copyright year: 1996
Publisher: Brooks/Cole
Publication date: 9/8/1995
Binding: Hardcover
Pages: 54
Size: 8.00" wide x 9.75" long x 1.25" tall
Weight: 2.750

Preface
List of Applications
Introduction to Linear Equations and Matrices
Introduction to Linear Systems and Matrices
Gaussian Elimination
The Algebra of Matrices: Four Descriptions of the Product
Inverses and Elementary Matrices
Gaussian Elimination as a Matrix Factorization
Transposes, Symmetry, and Band Matrices: An Application
Numerical and Programming Considerations: Partial Pivoting, Overwriting Matrices, and Ill-Conditioned Systems
Review Exercises
Determinants
The Determinant Function
Properties of Determinants
Finding det A Using Signed Elementary Products
Cofactor Expansion: Cramer's Rule
Applications
Review Exercises
Vector Spaces
Vectors in 2- and 3-Spaces
Euclidean n-Space
General Vector Spaces
Subspaces, Span, Null Spaces
Linear Independence
Basis and Dimension
The Fundamental Subspaces of a Matrix
Rank
Coordinates and Change of Basis
An Application: Error-Correcting Codes
Review Exercises
Cumulative Review Exercises
Linear Transformations, Orthogonal Projections and Least Squares
Matrices as Linear Transformation
Relationships Involving Inner Products
Least Squares and Orthogonal Projections
Orthogonal Bases and the Gram-Schmidt Process
Orthogonal Matrices, QR Decompositions, and Least Squares (Revisited)
Encoding the QR Decompositions: A Geometric Approach
General Matrices of Linear of Linear Transformations
Similarity
Review Exercises
Cumulative Review Exercises
Eigenvectors and Eigenvalues
A Brief Introduction to Determinants
Eigenvalues and Eigenvectors
Diagonalization
Symmetric Matrices
An Application - Difference Equations: Fibonacci Sequences and Markov Processes
An Application -Differential Equations
An Application -- Quadratic Forms
Solving the Eigenvalue Problem Numerically
Review Exercises
Cumulative Review Exercises
Further Directions
Function Spaces
The Singular Value Decomposition -- Generalized Inverses, the General Least-Squares Problem, and an Approach to Ill-Conditioned Systems
Iterative Method
Matrix Norms
General Vector Spaces and Linear Transformations Over an Arbitrary Field
Review Exercises
More on LU Decompositions
Counting Operations and Gauss-Jordan Elimination
Another Application
Introduction to MATLAB and Projects
Bibliography and Further Readings
Index

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