Elementary Linear Algebra

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  • Edition: 2nd
  • Format: Hardcover
  • Copyright: 2007-06-01
  • Publisher: Pearson
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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

Prefacep. xi
To the Studentp. xvii
Matrices, Vectors, and Systems of Linear Equationsp. 3
Matrices and Vectorsp. 3
Linear Combinations, Matrix-Vector Products, and Special Matricesp. 13
Systems of Linear Equationsp. 27
Gaussian Eliminationp. 41
Applications of Systems of Linear Equationsp. 56
The Span of a Set of Vectorsp. 66
Linear Dependence and Linear Independencep. 75
Review Exercisesp. 87
MATLAB Exercisesp. 90
Matrices and Linear Transformationsp. 95
Matrix Multiplicationp. 95
Applications of Matrix Multiplicationp. 106
Invertibility and Elementary Matricesp. 122
The Inverse of a Matrixp. 135
Partitioned Matrices and Block Multiplicationp. 146
The LU Decomposition of a Matrixp. 152
Linear Transformations and Matricesp. 167
Composition and Invertibility of Linear Transformationsp. 180
Review Exercisesp. 192
MATLAB Exercisesp. 195
Determinantsp. 199
Cofactor Expansionp. 199
Properties of Determinantsp. 211
Review Exercisesp. 222
MATLAB Exercisesp. 224
Subspaces and their Propertiesp. 227
Subspacesp. 227
Basis and Dimensionp. 241
The Dimension of Subspaces Associated with a Matrixp. 254
Coordinate Systemsp. 263
Matrix Representations of Linear Operatorsp. 275
Review Exercisesp. 286
MATLAB Exercisesp. 288
Eigenvalues, Eigenvectors, and Diagonalizationp. 293
Eigenvalues and Eigenvectorsp. 293
The Characteristic Polynomialp. 302
Diagonalization of Matricesp. 313
Diagonalization of Linear Operatorsp. 325
Applications of Eigenvaluesp. 334
Review Exercisesp. 355
MATLAB Exercisesp. 356
Orthogonalityp. 361
The Geometry of Vectorsp. 361
Orthogonal Vectorsp. 374
Orthogonal Projectionsp. 388
Least-Squares Approximation and Orthogonal Projection Matricesp. 402
Orthogonal Matrices and Operatorsp. 411
Symmetric Matricesp. 425
Singular Value Decompositionp. 438
Principal Component Analysisp. 456
Rotations of R[superscript 3] and Computer Graphicsp. 465
Review Exercisesp. 481
MATLAB Exercisesp. 483
Vector Spacesp. 489
Vector Spaces and Their Subspacesp. 489
Linear Transformationsp. 501
Basis and Dimensionp. 511
Matrix Representations of Linear Operatorsp. 521
Inner Product Spacesp. 532
Review Exercisesp. 547
MATLAB Exercisesp. 548
Appendicesp. 551
Setsp. 551
Functionsp. 553
Complex Numbersp. 556
MATLABp. 561
The Uniqueness of the Reduced Row Echelon Formp. 575
Bibliographyp. 579
Answers to Selected Exercisesp. 581
Indexp. 621
Table of Contents provided by Ingram. All Rights Reserved.

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