9780395967171

Elementary Linear Algebra

by Unknown
  • ISBN13:

    9780395967171

  • ISBN10:

    0395967171

  • Edition: 4th
  • Format: Paperback
  • Copyright: 6/15/1999
  • Publisher: Brooks Cole
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Summary

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.

Table of Contents

What is Linear Algebra? xiii
Systems of Linear Equations
1(41)
Biographical Sketch of Carl Friedrich Gauss
1(1)
Introduction to Systems of Linear Equations
1(12)
Gaussian Elimination and Gauss-Jordan Elimination
13(14)
Applications of Systems of Linear Equations
27(15)
Chapter Summary
37(1)
Review Exercises
38(2)
Projects
40(2)
Matrices
42(69)
Biographical Sketch of Arthur Cayley
42(1)
Operations with Matrices
42(13)
Properties of Matrix Operations
55(11)
The Inverse of a Matrix
66(13)
Elementary Matrices
79(11)
Applications of Matrix Operations
90(21)
Chapter Summary
105(1)
Review Exercises
106(3)
Projects
109(2)
Determinants
111(49)
Biographical Sketch of Augustin-Louis Cauchy
111(1)
The Determinant of a Matrix
111(9)
Evaluation of a Determinant Using Elementary Operations
120(9)
Properties of Determinants
129(8)
Applications of Determinants
137(23)
Chapter Summary
152(1)
Review Exercises
153(1)
Projects
153(5)
Cumulative Test for Chapters 1--3
158(2)
Vector Spaces
160(90)
Biographical Sketch of William Rowan Hamilton
160(1)
Vectors in Rn
160(10)
Vectors Spaces
170(8)
Subspaces of Vector Spaces
178(8)
Spanning Sets and Linear Independence
186(12)
Basis and Dimension
198(11)
Rank of a Matrix and Systems of Linear Equations
209(15)
Coordinates and Change of Basis
224(11)
Applications of Vector Spaces
235(15)
Chapter Summary
244(1)
Review Exercises
245(3)
Projects
248(2)
Inner Product Spaces
250(75)
Biographical Sketch of Jean-Baptiste Joseph Fourier
250(10)
Length and Dot Product in Rn
260(4)
Inner Product Spaces
264(12)
Orthonormal Bases: Gram-Schmidt Process
276(12)
Mathematical Models and Least Squares Analysis
288(14)
Applications of Inner Product Spaces
302(23)
Chapter Summary
316(1)
Review Exercises
317(2)
Projects
319(3)
Cumulative Test for Chapters 4 and 5
322(3)
Linear Transformations
325(54)
Biographical Sketch of Emmy Noether
325(1)
Introduction to Linear Transformations
325(12)
The Kernel and Range of a Linear Transformation
337(12)
Matrices for Linear Transformations
349(11)
Transition Matrices and Similarity
360(6)
Applications of Linear Transformations
366(13)
Chapter Summary
374(1)
Review Exercises
375(2)
Projects
377(2)
Eigenvalues and Eigenvectors
379(1)
Biographical Sketch of James Joseph Sylvester
379(1)
Eigenvalues and Eigenvectors
379(13)
Diagonalization
392(10)
Symmetric Matrices and Orthogonal Diagonalization
402(12)
Applications of Eigenvalues and Eigenvectors
414(15)
Chapter Summary
429(1)
Review Exercises
430(2)
Projects
432(2)
Cumulative Test for Chapters 6 and 7
434
Appendices A1
A Mathematical Induction and Other Forms of Proofs
A1
B Computer Algebra Systems and Graphing Calculators
A9
Answer Key A20
Index A58

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