Elementary Linear Algebra

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  • Edition: 5th
  • Format: Hardcover
  • Copyright: 2003-06-04
  • Publisher: Brooks Cole
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The hallmark of this text has been the authors' clear, careful, and concise presentation of linear algebra so that students can fully understand how the mathematics works. The text balances theory with examples, applications, and geometric intuition. Learning Tools CD-ROM will be automatically packaged free with every new text purchased from Houghton Mifflin. Section 3.4, now named "Introduction to Eigenvalues," has been broken into two separate sections to provide more emphasis on the early introduction of eigenvalues. The new Section 3.5, "Applications of Determinants," covers the Adjoint of a Matrix; Cramer's Rule; and the Area, Volume, and Equations of Lines and Planes. All real data in exercises and examples have been updated to reflect current statistics and information. This edition features more Writing Exercises to reinforce critical-thinking skills and additional multi-part True/False Questions in the end-of-section and chapter review exercise sets to encourage students to think about mathematics from different perspectives. Additional exercises involving larger matrices have been added to the exercise sets where appropriate. These exercises will be linked to the data sets found on the web site and the Learning Tools CD-ROM. Eduspace is Houghton Mifflin's online learning tool. Powered by Blackboard, Eduspace is a customizable, powerful and interactive platform that provides instructors with text-specific online courses and content. The Larson Elementary Linear Algebra course features algorithmic exercises and test bank content in question pools.

Table of Contents

Note: Each chapter concludes with a Chapter Summary, Review Exercises, and Projects. What Is Linear Algebra?
Systems of Linear Equations Biographical Sketch of Carl Friedrich Gauss
Introduction to Systems of Linear Equations
Gaussian Elimination and Gauss-Jordan Elimination
Applications of Systems of Linear Equations
Matrices Biographical Sketch of Arthur Cayley
Operations with Matrices
Properties of Matrix Operations
The Inverse of a Matrix
Elementary Matrices
Applications of Matrix Operations
Determinants Biographical Sketch of Augustin-Louis Cauchy
The Determinant of a Matrix
Evaluation of a Determinant Using Elementary Operations
Properties of Determinants
Introduction to Eigenvalues
Applications of Determinants Cumulative Test for Chapters 13
Vector Spaces Biographical Sketch of William Rowan Hamilton
Vectors in Rn
Vector Spaces
Subspaces of Vector Spaces
Spanning Sets and Linear Independence
Basis and Dimension
Rank of a Matrix and Systems of Linear Equations
Coordinates and Change of Basis
Applications of Vector Spaces
Inner Product Spaces Biographical Sketch of Jean-Baptiste Joseph Fourier
Length and Dot Product in Rn
Inner Product Spaces
Orthonormal Bases: Gram-Schmidt Process
Mathematical Models and Least Squares Analysis
Applications of Inner Product Spaces Cumulative Test for Chapters 4 and 5
Linear Transformations Biographical Sketch of Emmy Noether
Introduction to Linear Transformations
The Kernel and Range of a Linear Transformation
Matrices for Linear Transformations
Transition Matrices and Similarity
Applications of Linear Transformations
Eigenvalues and Eigenvectors Biographical Sketch of James Joseph Sylvester
Eigenvalues and Eigenvectors
Symmetric Matrices and Orthogonal Diagonalization
Applications of Eigenvalues and Eigenvectors Cumulative Test for Chapters 6 and 7
Complex Vector Spaces* Biographical Sketch of Charles Hermite
Complex Numbers
Conjugates and Division of Complex Numbers
Polar Form and DeMoivre's Theorem
Complex Vector Spaces and Inner Products
Unitary and Hermitian Matrices
Linear Programming* Biographical Sketch of John von Neumann
Systems of Linear Inequalities
Linear Programming Involving Two Variables
The Simplex Method: Maximization
The Simplex Method: Minimization
The Simplex Method: Mixed Constraints
Numerical Methods
Biographical Sketch of Carl Gustav Jacob Jacobi
Gaussian Elimination with Partial Pivoting
Interative Methods for Solving Linear Systems
Power Method for Approximating Eigenvalues
Applications of Numerical Methods
Mathematical Induction and Other Forms of Proofs
Computer Algebra Systems and Graphing Calculators
Answer Key Index * Chapters 8, 9, and 10 are available on the Learning Tools Student CD-ROM and the textbook web site
Table of Contents provided by Publisher. All Rights Reserved.

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