Elementary Linear Algebra

by Spence, Lawrence E.; Insel, Arnold J.; Friedberg, Stephen H.

• ISBN13: 9780131871410
• ISBN10: 0131871412
• Edition: 2nd
• Format: Hardcover
• Copyright: 2007-06-01
• Publisher: Pearson

Summary

Ideal as a reference or quick review of the fundamentals of linear algebra, this book offers amatrix-oriented approach--with more emphasis on Euclidean n-space, problem solving, and applications, and less emphasis on abstract vector spaces. It features a variety of applications, boxed statements of important results, and a large number of numbered and unnumbered examples.Matrices, Vectors, and Systems of Linear Equations. Matrices and Linear Transformations. Determinants. Subspaces and Their Properties. Eigenvalues, Eigenvectors, and Diagonalization. Orthogonality. Vector Spaces. Complex Numbers.A professional reference for computer scientists, statisticians, and some engineers.

Table of Contents

Preface	p. xi
To the Student	p. xvii
Matrices, Vectors, and Systems of Linear Equations	p. 3
Matrices and Vectors	p. 3
Linear Combinations, Matrix-Vector Products, and Special Matrices	p. 13
Systems of Linear Equations	p. 27
Gaussian Elimination	p. 41
Applications of Systems of Linear Equations	p. 56
The Span of a Set of Vectors	p. 66
Linear Dependence and Linear Independence	p. 75
Review Exercises	p. 87
MATLAB Exercises	p. 90
Matrices and Linear Transformations	p. 95
Matrix Multiplication	p. 95
Applications of Matrix Multiplication	p. 106
Invertibility and Elementary Matrices	p. 122
The Inverse of a Matrix	p. 135
Partitioned Matrices and Block Multiplication	p. 146
The LU Decomposition of a Matrix	p. 152
Linear Transformations and Matrices	p. 167
Composition and Invertibility of Linear Transformations	p. 180
Review Exercises	p. 192
MATLAB Exercises	p. 195
Determinants	p. 199
Cofactor Expansion	p. 199
Properties of Determinants	p. 211
Review Exercises	p. 222
MATLAB Exercises	p. 224
Subspaces and their Properties	p. 227
Subspaces	p. 227
Basis and Dimension	p. 241
The Dimension of Subspaces Associated with a Matrix	p. 254
Coordinate Systems	p. 263
Matrix Representations of Linear Operators	p. 275
Review Exercises	p. 286
MATLAB Exercises	p. 288
Eigenvalues, Eigenvectors, and Diagonalization	p. 293
Eigenvalues and Eigenvectors	p. 293
The Characteristic Polynomial	p. 302
Diagonalization of Matrices	p. 313
Diagonalization of Linear Operators	p. 325
Applications of Eigenvalues	p. 334
Review Exercises	p. 355
MATLAB Exercises	p. 356
Orthogonality	p. 361
The Geometry of Vectors	p. 361
Orthogonal Vectors	p. 374
Orthogonal Projections	p. 388
Least-Squares Approximation and Orthogonal Projection Matrices	p. 402
Orthogonal Matrices and Operators	p. 411
Symmetric Matrices	p. 425
Singular Value Decomposition	p. 438
Principal Component Analysis	p. 456
Rotations of R[superscript 3] and Computer Graphics	p. 465
Review Exercises	p. 481
MATLAB Exercises	p. 483
Vector Spaces	p. 489
Vector Spaces and Their Subspaces	p. 489
Linear Transformations	p. 501
Basis and Dimension	p. 511
Matrix Representations of Linear Operators	p. 521
Inner Product Spaces	p. 532
Review Exercises	p. 547
MATLAB Exercises	p. 548
Appendices	p. 551
Sets	p. 551
Functions	p. 553
Complex Numbers	p. 556
MATLAB	p. 561
The Uniqueness of the Reduced Row Echelon Form	p. 575
Bibliography	p. 579
Answers to Selected Exercises	p. 581
Index	p. 621
Table of Contents provided by Ingram. All Rights Reserved.