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9780132663137

Introductory Linear Algebra With Applications

by ;
  • ISBN13:

    9780132663137

  • ISBN10:

    0132663139

  • Edition: 6th
  • Format: Hardcover
  • Copyright: 1997-02-01
  • Publisher: Prentice Hall Professional Technical Reference
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Supplemental Materials

What is included with this book?

Summary

This is the easier of Kolman's two texts: it has more applications and vector spaces come later in the text. Major revision. New edition is most technology friendly book in this market. Last chapter is on numerical techniques using MATLAB. Also has superb MATLAB manual by Hill/Zitarelli ('96) that should be sampled to anyone interested in technology.

Table of Contents

Preface xi
Part I INTRODUCTORY LINEAR ALGEBRA 3(368)
1 Linear Equations and Matrices
3(88)
1.1 Linear Systems
3(8)
1.2 Matrices
11(7)
1.3 Dot Product and Matrix Multiplication
18(17)
1.4 Properties of Matrix Operations
35(12)
1.5 Solutions of Linear Systems of Equations
47(22)
1.6 The Inverse of a Matrix
69(22)
2 Determinants
91(32)
2.1 Definition and Properties
91(12)
2.2 Cofactor Expansion and Applications
103(15)
2.3 Determinants from a Computational Point of View
118(5)
3 Vectors in R(2) and R(n)
123(74)
3.1 Vectors in the Plane
123(18)
3.2 n-Vectors
141(17)
3.3 Introduction to Linear Transformations
158(13)
3.4 Computer Graphics (Optional)
171(8)
3.5 Cross Product in R(3) (Optional)
179(7)
3.6 Lines and Planes
186(11)
4 Real Vector Spaces
197(94)
4.1 Real Vector Spaces
197(6)
4.2 Subspaces
203(10)
4.3 Linear Independence
213(11)
4.4 Basis and Dimension
224(13)
4.5 Homogeneous Systems
237(7)
4.6 The Rank of a Matrix and Applications
244(11)
4.7 Coordinates and Change of Basis
255(14)
4.8 Orthonormal Bases in R(n)
269(8)
4.9 Orthogonal Complements
277(14)
5 Eigenvalues and Eigenvectors
291(36)
5.1 Diagonalization
291(21)
5.2 Diagonalization of Symmetric Matrices
312(15)
6 Linear Transformations and Matrices
327(39)
6.1 Definition and Examples
327(7)
6.2 The Kernel and Range of a Linear Transformation
334(11)
6.3 The Matrix of a Linear Transformation
345(21)
Cumulative Review of Part I
366(5)
Part II APPLICATIONS 371(164)
7 Linear Programming
371(46)
7.1 The Linear Programming Problem; Geometric Solution
371(18)
7.2 The Simplex Method
389(19)
7.3 Duality
408(9)
8 Applications
417(118)
8.1 Graph Theory
417(17)
8.2 Electrical Circuits
434(5)
8.3 Markov Chains
439(11)
8.4 Least Squares
450(11)
8.5 Linear Economic Models
461(8)
8.6 Differential Equations (Calculus Required)
469(11)
8.7 The Fibonacci Sequence
480(4)
8.8 Quadratic Forms
484(9)
8.9 Conic Sections
493(8)
8.10 Quadric Surfaces
501(10)
8.11 The Theory of Games
511(24)
Part III NUMERICAL LINEAR ALGEBRA 535(38)
9 Numerical Linear Algebra
535(38)
9.1 Error Analysis
535(3)
9.2 Linear Systems
538(11)
9.3 LU-Factorization (Optional)
549(7)
9.4 QR-Factorization (Optional)
556(5)
9.5 Eigenvalues and Eigenvectors
561(12)
Part IV MATLAB FOR LINEAR ALGEBRA 573
10 MATLAB for Linear Algebra
573
10.1 Input and Output in MATLAB
573(6)
10.2 Matrix Operations in MATLAB
579(3)
10.3 Matrix Powers and Some Special Matrices
582(3)
10.4 Elementary Row Operations in MATLAB
585(10)
10.5 Matrix Inverses in MATLAB
595(1)
10.6 Vectors in MATLAB
596(2)
10.7 Applications of Linear Combinations in MATLAB
598(4)
10.8 Linear Transformations in MATLAB
602(2)
10.9 MATLAB Command Summary
604
Appendix A Complex Numbers A1
A.1 Complex Numbers A1
A.2 Complex Numbers in Linear Algebra A10
Appendix B Further Directions A23
B.1 Inner Product Spaces (Calculus Required) A23
B.2 Composite and Invertible Linear Transformations A32
Answers to Odd-Numbered Exercises and Chapter Tests A41
Index I1

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